Efficient computation of the Discrete Fourier Transform (DFT) for signals with structured frequency support remains a significant challenge in signal processing. The traditional Fast Fourier Transform (FFT) algorithm achieves O(NlogN) complexity, but substantial improvements are possible for signals with known structured supports. In prior work, Pochimireddy et al. demonstrated that for signals with homogeneous supports and a length N that is a power of a prime, the DFT can be computed in O(klogk) time, where k is the size of the frequency support. However, this work was restricted signals with specific lengths. This paper extends these results by developing algorithms for signals of arbitrary lengths using circular convolution techniques to achieve the same computational efficiency. Our proposed methods enhance the theoretical framework and practical utility of structured DFT computation, extending the range of applicable signal lengths. Numerous examples demonstrate the effectiveness of our approach, paving the way for more efficient signal processing in various modern applications.

In this paper, we present a novel operator designed to handle the shifting of multiple periodic signals. By exploiting the unique properties of the companion matrix and the elegant structure of cyclotomic polynomials, we have developed an efficient and versatile tool for signal processing applications. The proposed operator can be further utilized to design an FIR filter for decomposition and separation of different period mixed signals.

In this paper, we investigate the intriguing connection between the Discrete Cosine Transform (DCT) and integral graphs, contributing to the field of signal processing on graphs. Throughout our investigation, we discover two types of novel integral graphs based on DCT. The first type emerges as a result of Ramanujan’s Sum, and interestingly, we establish its isomorphism with the DFT-based approach. The second type arises from fundamental properties of DCT, representing a unique and valuable contribution.

We investigate the reconstruction of a binary image from its sparse 2D discrete Fourier transform (2D-DFT) coefficients. Specifically, we focus on the case where the image height is equal to its width and is a prime number. We derive a lower bound on the number of coefficients required for perfect image recovery and propose a reconstruction algorithm. In our experiment, we demonstrate that the lower bound can be achieved when the height is less than 20. Consequently, we can efficiently reconstruct a 19×19 binary image using only 21 out of the total 361 2D-DFT coefficients, which accounts for approximately 5.81% of the coefficients..

Tone-mapping plays an essential role in high dynamic range (HDR) imaging. It aims to preserve visual information of HDR images in a medium with a limited dynamic range. Although many works have been proposed to provide tone-mapped results from HDR images, most of them can only perform tone-mapping in a single pre-designed way. However, the subjectivity of tone-mapping quality varies from person to person, and the preference of tone-mapping style also differs from application to application. In this paper, a learning-based multimodal tone-mapping method is proposed, which not only achieves excellent visual quality but also explores the style diversity. Based on the framework of BicycleGAN [1], the proposed method can provide a variety of expert-level tone-mapped results by manipulating different latent codes. Finally, we show that the proposed method performs favorably against state-of-the-art tone-mapping algorithms both quantitatively and qualitatively.

In this article a low complexity and accurate frequency estimation method for 2D signals is proposed. It can be applied to antenna array signal processing and image processing. This method is very efficient because it only samples two 1D lines in first dimension. The corresponding frequency in the second dimension is estimated by phase difference and fine-tuned by sampling another line. Through experiments, we found it effective in noise removal. To conclude, the proposed method is suitable for 2D accurate frequency estimation and preprocessing.

The recent super-resolution (SR) techniques are divided into two directions. One is to improve PSNR and the other is to improve visual quality. We believe improving visual quality is more important and practical than blindly improving PSNR. In this paper we employ a generative adversarial network (GAN) and a new perceptual loss function for photo-realistic single image super-resolution (SISR). Our main contributions are as follows: we propose a new dense block which uses complex connections between each layer to build a more powerful generator. Next, to improve the perceptual quality, we found a new set of feature maps to compute the perceptual loss, which would make the output image look more real and natural. Finally, we compare our results with other methods by subjective evaluation. The subjects rank the image generated by various methods from good to bad. The final results show that our method can generate a more natural and realistic SR image than other state-of-the-art methods.

Deep convolutional neural networks (DCNN) have demonstrated their potential to generate reasonable results in image inpainting. Some existing method uses convolution to generate surrounding features, then passes features by fully connected layers, and finally predicts missing regions. Although the final result is semantically reasonable, some blurred situations generated because the standard convolution is used, which conditioned on the effective pixels and the substitute values in the masked holes. In this paper, we introduce dense blocks for the U-Net architecture, which can alleviate the problem of gradient disappearance, while also reducing the number of parameters. The most important is that it can enhance the transfer of features and make more efficient use of them. Partial convolution is used to solve the problem of artifacts such as color differences and blurring. Experiments on the place365 dataset demonstrate our approach can generate more detailed and semantically reasonable results in random area image inpainting.

In this work, we focus on building style transfer, which transforms ruin or old buildings to modern architecture. Inspired by Gaty's and Goodfellow's style transfer and generative adversarial network (GAN), we use CycleGAN to conquer this type of problem. As we know, image style transfer usually generated unexpected artifacts. To avoid the artifacts and generate better images, we add so called “perception loss” into the network, which is the feature loss extracted by VGG pre-trained model. In the part of “cycle” structure, we adjust cycle loss by changing the ratio of weighting parameters. Finally, we collect images of both ruin (or old) and modern architecture from websites and use unsupervised learning to train the model. The experimental results show our proposed method indeed realize the modern architecture style transfer for ruin or old buildings.

Objective assessment for videos has developed with mature technique. However, there are still some challenges, such as mimicking the behavior that human-beings do when they watch a video. In this paper, we introduce a model for full-reference (FR) video quality assessment (VQA) which is based on visual attention, optical flow, spatio-temporal slice (STS) images and center bias map. The experimental results show that our proposed model has better performance in wireless transmission distortion than other models in the LIVE video quality database.

Inspired by Gatys and Goodfellow's style transfer and generative adversarial network (GAN), we use CycleGAN to achieve age progression. CycleGAN is good at generating fake images and also competitive with other GANs. It not only generates fake images but also increases the number of images in our database. We know the better database, the better performance of the model. We also try a deeper generator to transform youth photos to elder photos. To avoid the artifacts, we not only adopt the idea of “cycle” but also add a new loss which can tell the discriminator not too strict to generated images. Finally, we collect images of young and old people from the Internet and use unsupervised learning to train our model. The experimental results show our proposed method is indeed improved and better than before.

A novel method is proposed to construct arbitrary length perfect integer sequences based on all-pass polynomial. It uses a fact that associative sequence of an all-pass polynomial is guaranteed to be perfect. In addition, geometric series method is our special case. Moreover, perfect Gaussian integer sequences can also be constructed. Furthermore, this approach can be applied to symmetric perfect sequences design. Finally, perfect sequence with low degree of freedom can be achieved by the difference set. Concrete examples are illustrated.

In this paper, we propose an adaptive STFT (ASTFT) with adaptive chirp-modulated Gaussian window. The window is obtained from rotating Gaussian function in time-frequency plane by fractional Fourier transform (FRFT). It is completely adaptive where the two parameters, FRFT rotation angle and Gaussian variance, are signal-dependent. The angle dependents on the chirp rate of the signal. The variance is determined by the chirp rate and its first derivative. Considering the input may be multicomponent, a chirp-modulated Gaussian window with time-frequency-varying angle and variance is developed. The proposed ASTFT has very high energy concentration and less interference between components in noiseless and noisy environments.

Compressive sensing (CS) is proposed for signal sampling below the Nyquist rate based on the assumption that the signal is sparse in some transformed domain. Most sensing matrices (e.g., Gaussian random matrix) in CS, however, usually suffer from unfriendly hardware implementation, high computation cost, and huge memory storage. In this letter, we propose a deterministic sensing matrix for collecting measurements fed into sparse fast Fourier transform (sFFT) as the decoder. Compared with the conventional paradigm with Gaussian random matrix at encoder and convex programming or greedy method at decoders, sFFT can reconstruct sparse signals with very low computation cost under the comparable number of measurements. But, the limitation is that the signal must be sparse in the frequency domain. We further show how to relax this limitation into any domains with the transformation matrix or dictionary being circulant. Experimental and theoretical results validate that the proposed method achieves fast sensing, fast recovery, and low memory cost.

In this letter, a novel method is proposed to generate discrete approximations of continuous Hermite-Gaussian functions with noninteger shift and dilation. Moreover, the approximations preserve orthogonality. In addition, the discrete Hermite-Gaussian functions reach the minimum time-bandwidth product under discrete version of Gabor uncertainty principle. Two applications are demonstrated. In fractional delay application, the proposed method is compared with the windowing method and proved to have smaller delay error. Another one is the signal expansion based on the proposed complete orthogonal basis.

In this paper, we propose a novel descriptor for face recognition on grayscale images, depth images and 2D+depth images. It is a compact and effective descriptor computed from the magnitude and the direction difference. It can be concatenated with conventional descriptors such as well-known Local Binary Pattern (LBP) and Weber Local Binary Pattern (WLBP), to enhance their discrimination capability. To evaluate the performance of our descriptor, we conducted extensive experiments on three types of images using four different databases. The experimental results demonstrate the robustness and superiority of our approach, and the performances of our new descriptor surpass that without magnitude and direction difference. At the end, we further compare our descriptor with Convolution Neural Network (CNN) to show the compactness and effectiveness of the proposed approach.

In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram-Schmidt process from the Ramanujan sum and its circular shift. It has a surprisingly simple and sparse form, which is better than the original complete Ramanujan basis. The relationship between the original basis and proposed basis is also clearly illustrated. Therefore, the original basis can be replaced easily.

In this paper, we propose an image enhancement system to maintain human visual perception for low-backlighted LCD or LED displays. Adopting the low-backlight mode can save electrical power and extend battery life. First, we examine the relationship between the image and backlight to maintain visual perceptual quality. Then, we use an adaptive illumination estimation to decompose the image intensity into an illumination layer and a reflectance layer with multiscale and parallel perspectives. We then refer to the given backlight level and our derived image-backlight relationship to compensate the illumination layer and meanwhile enhance the reflectance layer. Finally, we also boost the color saturation. Experiments using both numerical blind/referenceless image spatial quality evaluator and subjective mean opinion score demonstrate that our system outperforms existing systems.

Linear canonical transform (LCT) is an attractive and useful tool in optics and signal processing. In previous work, a generalization of the LCT with two extra parameters, called offset LCT (OLCT), has been developed. In this paper, a different definition of OLCT is proposed, which has a more concise form of inverse transform. We find a linear operator that commutes with the proposed OLCT. We prove that the commuting operator and the proposed OLCT have the same set of eigenfunctions with different eigenvalues. We also derive the discrete version of the commuting operator to develop a discrete OLCT. The proposed discrete OLCT has perfect reversibility property.

Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast embedding scheme by first downsampling N-dimensional data into M-dimensional data and then multiplying the data with an M×M circulant matrix. Our method requires O(N + M log M) computation and O(N) storage costs. We prove if data have sparsity, our scheme can achieve similarity-preserving well. Experiments further demonstrate that though our method is cost-effective and fast, it still achieves comparable performance in image applications.

In this paper, we propose a new divide-and-conquer based method, called fusion of multiple binary age-grouping-estimation systems, for human facial age estimation. Under a specific constraint, such as a given facial feature or classification/regression method, what is the better framework for age estimation? First we employ multiple binary-grouping systems for age group classification. Each face image will be classified into one of the two groups. Within the two groups, two models are trained to estimate ages for the faces classified into their groups, respectively. We also investigate the effect of different age grouping systems on the performance of age grouping accuracy and age estimation error. In the last stage, we propose a sequentially selection algorithm to fuse some of the binary-grouping systems to get a final age estimation result. Experiments on the MORPH2 database demonstrate our framework for age estimation can achieve satisfying results and outperform other state-of-the-art age estimation approaches.

In this paper, a general feedback structure is proposed to improve the performance of existing digital notch filters. With the feedback structure, the notch filter can have a narrower stopband. This structure can be applied to any type of existing notch filter. We first derive the improved design of existing one-dimensional (1-D) filters. Then, by suitably extending the 1-D concept, the design of two-dimensional (2-D) notch filters is also derived. To demonstrate the effectiveness of the proposed design, an experiment on the interference removal of an image is presented. Moreover, a new forward and reverse algorithm for 2-D image filtering is proposed to reduce the transient error and enhance the signal-to-noise ratio drastically.

We propose a power-constrained image enhancement system to maintain human visual perception when the LCD or LED display is under low backlight. Adopting the low backlight mode can save the electricity and lengthen the battery using time. First, we deduce the relationship between the image and the backlight for maintaining the same visual perceptual quality. Then, we propose a sparsity-based image decomposition to separate the intensity image into base layer and detail layer. Afterwards, we refer to the image-backlight relationship to compensate the base layer, while we also adopt texture-aw are boosting to enhance the detail layer. Experimental simulated results show that our system outperforms than the compared systems.

A novel method to generate integer 2-D discrete Fourier transform (DFT) pairs and eigenvectors was proposed. Using projection slice theorem and Ramanujan's sum, the 2-D spatial signal is decomposed into 2-D gcd-delta functions which contain only zeroes and ones. The 2-D DFT of 2-D gcd-delta functions are also integers. The integer 2-D DFT pairs can be applied to obtain integer 2-D DFT eigenvectors and 2-D period detection. The connection between 2-D gcd-delta function and multidimensional Ramanujan's Sum is also illustrated with two numerical examples.

This paper presents a comparison study on subjective quality scores obtained by both single stimulus (without reference) and triple stimulus (with reference) methods. The TID2013 database is reevaluated by single stimulus approach, which is realized by absolute category rating (ACR). And the mean opinion score (MOS) provided along with TID2013 represents the results from triple-stimulus pair comparison (3-stimulus PC) method. In the end, the correlation coefficient and hypothesis testing are used to determine if there is a significant difference between both sets of scores. The experimental results show that the differences exist and are significant for some specific distortion types or image contents. We believe the findings in this work can benefit and facilitate the future subjective visual quality viewing tests.

This work presents a novel facial makeup detection method, which includes four steps: entropy information computation, feature extraction, feature selection and classification. To carry out this objective, first all face images are subject to the entropy information computation. Once the entropy images of faces are obtained, a feature extraction step is applied to the entropy images instead of original face images. The extracted features are further processed to reduce the redundant information on the feature vector, which is done by a feature selection procedure. A statistical analysis approach is chosen to realize this feature selection purpose, which aims to lower the feature dimension and maintain higher discrimination. In the last step, the makeup is detected by classifying faces into two groups: makeup and no-makeup. The experimental results on two databases indeed demonstrate the superiority of the proposed method.

Color correction or stabilization methods for image and video are important in signal processing areas. We can obtain image and video with better quality and more pleasing appearance by applying these correction methods. Besides, color corrected image and video also can be used to enhance performance of many post-processing techniques, such as pattern recognition, object tracking, human face matching, etc. In this paper, we have proposed a color correction algorithm based on quaternion algebra for color image and video. First, our method uses quaternion color distance metric to compute the pixel-based color differences between target image (or video frame) and reference image/video frame with similar appearance but slightly different illumination condition. After the color differences of image pixels are obtained, we use these pixels to calculate a correction matrix and use this matrix to correct target image and video frame. Our method can be applied to image and video with fast processing speed and has good performance when compared it with state-of-the-art method in the literature. The algorithm is also simple, effective, and easy to be implemented.

Affine transformations of images are common used in modern signal processing, image processing, and computer graphics areas. Take rotation of images for example, we have to calculate the positions of pixels after rotation and use methods like cubic, bilinear, and nearest neighbor interpolation to interpolate some pixels in between. These interpolation and spatial-domain-based methods are slow, cumbersome and the PSNR (Peak signal to noise ratio) is also not satisfactory. In this paper, we propose frequency domain based method for Affine transformations by applying proposed fractional shift Fourier transform and modified inverse Fourier transform. For rotation of gray-scale images, three shearing matrices and fractional shift Fourier transform are applied to complete the task. Fast Fourier transform (FFT) algorithm can be used to implement Fourier transform and therefore our method is very fast and precise. For the general case, i.e. Affine transformations, we combine shearing matrices, fractional shift Fourier transform and Modified inverse Fourier transform method to achieve arbitrary Affine transformations with small distortion (above 50dB PSNR).

In this work, we describe some methods to generate zero autocorrelation Gauss integer sequences of arbitrary length. These methods can be combined with each other so that more choices can be made.

In this letter we focus on discrete integer-periodic signals, whose periodicity are different from the periodicity of continuous periodic signals in many aspects. We introduce a class of discrete periodic signals called intrinsic integer-periodic function (IIPF). An IIPF contains only a single period in terms of downsampling, which leads to some interesting properties for analyzing periodic components from a discrete signal. We show that one can use Ramanujan sum to decompose discrete periodic signals into IIPF components. Finally, we also propose an integer periodic spectrum rather than frequency spectrum. Our results show that the proposed integer periodic spectrum outperforms the conventional Ramanujan Fourier transform.

Objective image quality assessment (IQA) plays an important role in the development of multimedia applications. Prediction of IQA metric should be consistent with human perception. The release of the newest IQA database (TID2013) challenges most of the widely used quality metrics (e.g., peak-to-noise-ratio and structure similarity index). We propose a new methodology to build the metric model using a regression approach. The new IQA score is set to be the nonlinear combination of features extracted from several difference of Gaussian (DOG) frequency bands, which mimics the human visual system (HVS). Experimental results show that the random forest regression model trained by the proposed DOG feature is highly correspondent to the HVS and is also robust when tested by available databases.

In this paper, we propose a novel algorithm for high-definition displays to enlarge low-resolution images while maintaining perceptual constancy (i.e., the same field-of-view, perceptual blur radius, and the retinal image size in viewer's eyes). We model the relationship between a viewer and a display by considering two main aspects of visual perception, i.e., scaling factor and perceptual blur radius. As long as we enlarge an image while adjust its image blur levels on the display, we can maintain viewer's perceptual constancy. We show that the scaling factor should be set in proportion to the viewing distance and the blur levels on the display should be adjusted according to the focal length of a viewer. Toward this, we first refer to edge directions to interpolate a low-resolution image with the increasing of viewing distance and the scaling factor. After images are interpolated, we utilize a local contrast to estimate the spatially varying image blur levels of the interpolated image. We then further adjust the image blur levels using a parametric deblurring method, which combines L1 as well as L2 reconstruction errors, and Tikhonov with total variation regularization terms. By taking these factors into account, high-resolution images adaptive to viewing distance on a display can be generated. Experimental results on both natural image metric and user subjective studies across image scales demonstrate that the proposed super-resolution algorithm for high-definition displays performs favorably against the state-of-the-art methods.

In this paper, a novel data hiding scheme, 3D unseen visible watermarking (UVW) based on a depth no-synthesis-error (D-NOSE) model is proposed. The proposed method has the ability to detect and discover which region of a depth image is suitable for watermark embedding and calculate optimal variance in pixel values for watermarking. The watermark is embedded into the suitable region by modifying the depth map with optimal variation pixel values to ensure that the watermarked cover can be perceived the same as the original one with no synthesis error under normal rendering conditions. In the proposed UVW scheme, hidden information can be extracted successfully by the human visual system (HVS) when changing the rendering conditions. Experimental results prove that the proposed scheme has strong robustness and imperceptibility while depth distortions follow the thresholds derived from D-NOSE model. Practical applications and limitations of the proposed 3D UVW for auxiliary information delivery are also discussed in this paper.

This paper presents an approach to 3D rotation estimation using discrete spherical harmonic oscillator transforms (discrete SHOTs). Discrete SHOTs not only have simple and fast implementation methods but also are compatible with the existing angle estimation algorithms related to spherical harmonics. Discrete SHOTs of the rotated signal follow the same formulation to the Wigner-D matrix as spherical harmonics transforms. Thus, the spherical harmonics related algorithms could be utilized to discrete SHOTs without modification. Furthermore, compared to some existing methods, our approach with discrete SHOTs exhibits higher accuracy, higher precision and improved robustness to noise if the input signal is sampled uniformly on Cartesian grids. The phenomenon results from no interpolations in discrete SHOTs.

We propose a method to detect saliency from a single image using feature extraction and superpixel belief propagation. We observe that the previous works are hard to deal with the intrinsic material discontinuity and non-homogeneous color distribution within an object or a region. Motivated by this observation, we bring the belief propagation into the saliency detection. First, we separate the image into middle-level superpixels and also extract the low-level feature within each superpixel. Then, we build up a Markov-Random-Field (MRF) on the middle-level super-pixels and adopt propagation technique to optimize the superpixel saliency. Afterward, we refine this middle-level solution to per-pixel saliency map. Experimental results demonstrate that our proposed method is promising as compared to the state-of-the-art methods in both MSRA-1000 and SED datasets.

In earlier paper, a conjugate symmetric frequency response has been presented to design the variable fractional delay filter by FFT, and has been proved to associate with the windowed sinc filter. However, this earlier method has no transition band design consideration. Therefore, in this paper, the trade-off between the transition band width and Gibbs phenomenon ripples is discussed, and an improved closed form design with additional transition band samples is introduced to reduce Gibbs phenomenon ripples. The proposed improved fractional delay method can also be efficiently realized by FFT using the tunable fractional delay parameter and transition band weighting factor. Several comparisons between the earlier method and the proposed improved method are also demonstrated. By measuring the largest peak ripple value in magnitude responses, our proposed method can achieve 9.43 times peak ripples reduction than the earlier method.

We propose a parallel multi-scale retinex enhancement to synthesize a high-dynamic-range(HDR, HDR-like) image from a single low-dynamic-range (LDR) input. Since an image is composed of illumination and reflectance, we can enhance these two components to obtain our HDR results. First, we estimate the illumination from the input by optimizing a cost function with a spatially-adaptive edge prior. Then, we tune up the estimated illumination while enhance the reflection so as to synthesize the HDR result. In addition, we adopt parallel multi-scale acceleration for speed-up. Experimental results demonstrate that our retinex approach is promising as compared to the existing methods.

According to the observation that an image under the canonical light has a nearly neutral chromaticity distribution, an efficient three-step color correction approach is proposed: First, a preliminary color-corrected image is generated by linearly shifting the chromaticity distribution of an input image towards the neutral point. Then, a least square approximation formulation is presented to derive the illuminant color from the preliminary color-corrected image. Finally, based on the derived illuminant color and the Von Kries model, a refined color-corrected image can be obtained. From the experimental results on the widely-used SFU image dataset, the proposed approach could achieve comparable or even better performances against other well-known methods. In addition, several web images are examined to further demonstrate the effectiveness of our approach.

Sparse Fast Fourier Transform (sFFT) [1][2], has been recently proposed to outperform FFT in reducing computational complexity. Assume that an input signal of length N in the frequency domain is K-sparse, where K ≤ N. sFFT costs O(K logN) instead of O(N logN) in FFT. In this paper, a new fast sFFT algorithm is proposed and costs O(K logK) averagely without any operations being related to N. The idea is to downsample the original input signal at the beginning. Subsequent processing operates under downsampled signals, which length is proportional to O(K). However, downsampling possibly leads to “aliasing.” By shift theorem of DFT, the aliasing problem can be formulated as the “Moment-preserving problem.” In addition, a top-down iterative strategy combined with different downsampling factors further saves computational costs. Complexity analysis and experimental results show that our method outperforms FFT and sFFT.

In this paper, an improved color constancy approach is presented by considering the disadvantage of the well-known max-RGB algorithm: Only the unreliable maximum intensities are taken for illuminant estimation. To solve this problem, we propose the chromaticity neutralization process, which selects the representative pixels for robust illuminant computing. Moreover, to deal with the color deviation cases under multiple illuminant sources, we further present a procedure by first softly clustering the image pixels into several groups; the estimated illuminants from these groups are then combined based on the clustering weights to specifically determine the illuminant of each pixel. The experiments on two databases and web images demonstrate the effectiveness of our approach.

Properties of eigenvectors and eigenvalues for discrete Fourier transform (DFT) are important for defining and understanding the discrete fractional Fourier transform (DFRFT). In this paper, we first propose a closed-form formula to construct an eigenvector of N-point DFT by down-sampling and then folding any eigenvector of (4N)-point DFT. The result is then generalized to derive eigenvectors of N-point DFT from eigenvectors of (k2N)-point DFT. To show an application of the proposed new closed-form DFT eigenvectors, Hermite-Gaussian-like (HGL) DFT eigenvectors which are much closer to the continuous Hermite-Gaussian functions (HGFs) are computed from existing HGL DFT eigenvectors of larger sizes with computer experiments.

Recently, Color Filter Array (CFA) patterns are applied popularly in a digital camera. The CFA is a mosaic-like filter which only allows one primary color to be passed and captured by the sensor at each pixel, in order to save the cost. CFA will produce a mosaic-like color image and we have to use demosaicking algorithm to recover the original color image. In this paper, we propose a new method which uses Quaternion Fourier Transform (QFT) and low pass filter to do color image demosaicking. The proposed method is tested on several common CFA patterns and the efficacy of the proposed method is also demonstrated.

We propose a system to up-sample visual signals for high definition televisions (HDTVs). Although the original visual signals are degraded and limited, we still try to solve these problems by using super-resolution. First, we interpolate the visual signals with a edge taper to the desired size. Then, we combine L1 data term, L2 data term, Tikhonov-like regularizer and total variation regularizer with a saliency weighting for our L12TTV deblurring method. Adopting our L12TTV deblurring, we can remove the spatially-varying blurry conditions of the interpolated signals. Experimental results show that our system outperforms than comparisons in both image and video cases.

In the conventional JPEG algorithm, an image is divided into eight by eight blocks and then the 2-D DCT is applied to encode each block. In this paper, we find that, in addition to rectangular blocks, the 2-D DCT is also orthogonal in the trapezoid and triangular blocks. Therefore, instead of eight by eight blocks, we can generalize the JPEG algorithm and divide an image into trapezoid and triangular blocks according to the shapes of objects and achieve higher compression ratio. Compared with the existing shape adaptive compression algorithms, as we do not try to match the shape of each object exactly, the number of bytes used for encoding the edges can be less and the error caused from the high frequency component at the boundary can be avoided. The simulations show that, when the bit rate is fixed, our proposed algorithm can achieve higher PSNR than the JPEG algorithm and other shape adaptive algorithms. Furthermore, in addition to the 2-D DCT, we can also use our proposed method to generate the 2-D complete and orthogonal sine basis, Hartley basis, Walsh basis, and discrete polynomial basis in a trapezoid or a triangular block.

In this paper, the general form of the two-dimensional Fourier transform (2D FT) eigenfunctions is discussed. It is obtained from the linear combination of the 2D separable Hermite Gaussian functions (SHGFs). For example, the rotated Hermite Gaussian functions (RHGFs) for the rotated coordinate and the Laguerre Gaussian functions (LGFs) for the polar coordinate are two special cases of the general form. With the aid of the general form, we can achieve these 2D functions with perfect orthogonality. Finding the combination coefficients is equivalent to the multinomial expansion problem. Therefore, we can apply the fast Fourier transform and some recurrence relations to the coefficients. The computation cost is much less than the close-form coefficients, which is associated with the Jacobi polynomials.

A new transform, called the generalized fractional Fourier transform (gFrFT), is proposed. Originally, the eigenfunctions of the fractional Fourier transform (FrFT) are known as the Hermite Gaussian functions (HGFs). Besides, in optics, the HGFs are generalized to be the generalized Hermite Gaussian functions (gHGFs) and their adjoint functions (AgHGFs). Therefore, we can define the gFrFT by the eigenvalues of the FrFT and the eigenfunctions (gHGFs/AgHGFs) in the analysis or synthesis step. Four types of the gFrFT are defined and discussed. The integral forms of the gFrFTs are derived and they are closely related to some popular transforms, such as the Fourier transform (FT), the FrFT, and the complex linear canonical transform (CLCT). We can also extend the FT and the FrFT to the standard and elegant versions. Finally, some properties of the gFrFT are discussed.

In this paper, we propose a spatially-varying deblurring method to remove the out-of-focus blur. Our proposed method mainly contains three parts: blur map generation, image deblurring, and scale selection. First, we derive a blur map using local contrast prior and the guided filter. Second, we propose our image deblurring method with L1-2 optimization to obtain a better image quality. Finally, we adopt the scale selection to ensure our output free from ringing artifacts. The experimental results demonstrate our proposed method is promising.

We investigate the issue of content authentication for halftone videos transmitted over mobile devices. With an eye to the flickering that is the unique characteristic of halftone video and possesses the property of sparsity, a compressed sensing (CS)-based halftone video authentication method is presented. We show that the restricted isometry property (RIP) in CS can explain the principle of hash matching between two CS-based hashes. Promising results obtained from simulations demonstrate the feasibility of our method.

Removing nighttime haze technique is an important and necessary procedure to avoid ill-condition visibility of human eyes. To increase the visibility of the scene, there are some existing methods for dehazing in the daytime. Specifically, these methods have a satisfactory dehazing quality in the daytime but most of them are not all successful in the nighttime. In this paper, the proposed method can be properly applied nighttime haze images even they have some ill-properties of low overall contrast, low overall brightness, and “blue shift” airlight color. The basic concept of proposed method is to use color transfer [7], refined Dark Channel Prior (DCP), and Bilateral Filter in Local Contrast Correction (BFLCC)[5]. Experimental results show that the proposed method has the reliable capabilities for removing nighttime haze and attractive for some applications such as computer vision, vehicle, aviation and national defense security.

Removing haze technique is an important and necessary procedure to avoid ill-condition visibility of human eyes. To improve the dehazing quality, a new haze-removing method is proposed in this paper. Specifically, this method can be properly applied to various dense and distribution haze images without sacrificing color naturalness by using refined Dark Channel Prior(DCP) and adding post processing. Experimental results demonstrate that the new method provides higher dehazing quality and color naturalness than other existing techniques.

In this paper, we present an image decomposition method based on guided upper/lower envelops of the intensity signal. First, we estimate our upper/lower envelops by using a estimator guided by the gradient (edges). Second, using the guided envelops, we easily obtain the edge-preserving base layer of the intensity signal and its corresponding detail layer. In the end, we not only propose the JND-based detail boosting for image enhancement but also demonstrate our image abstraction/stylization. Experimental results show that our proposed method is promising as compared to the existing methods.

In this paper, we propose a new family orthogonal transforms defined over finite field called the Finite Field Orthogonal Transforms (FFOT). Unlike the traditional Number Theoretic Transform (NTT) that the relationship between the transform length and the field moduli has specific constraint in order to hold the orthogonality property, the FFOT has no such constraint so that the signal word length need not be limited by the transform length. In addition, the fast algorithm implementation like radix-2 Cooley-Tukey algorithm is also realizable for the FFOT and is suitable for fast data encryption.

In this letter, a novel tunable frequency response is proposed for variable fractional delay filter with careful consideration on conjugate symmetry. This proposed fractional delay method can be efficiently realized by FFT using the tunable fractional delay parameter. Its equivalent closed form to windowing method is derived and presented. Several comparisons to other windowing methods are also demonstrated, such as the magnitude response, group delay, and approximation error between ideal frequency response.

We propose a system to enhance the visual quality of displays under low backlight. Our system can not only prolong the battery life but also enhance visual quality. First, we propose a constrained L0 gradient image decomposition to separate base layer and detail layer. Afterwards, we design a median-preserving gamma correction for compensation and a JND-based boosting for detail enhancement. Experimental results show that our system outperforms than the compared systems.

Privacy has received considerable attention but is still largely ignored in the multimedia community. Consider a cloud computing scenario where the server is resource-abundant, and is capable of finishing the designated tasks. It is envisioned that secure media applications with privacy preservation will be treated seriously. In view of the fact that scale-invariant feature transform (SIFT) has been widely adopted in various fields, this paper is the first to target the importance of privacy-preserving SIFT (PPSIFT) and to address the problem of secure SIFT feature extraction and representation in the encrypted domain. As all of the operations in SIFT must be moved to the encrypted domain, we propose a privacy-preserving realization of the SIFT method based on homomorphic encryption. We show through the security analysis based on the discrete logarithm problem and RSA that PPSIFT is secure against ciphertext only attack and known plaintext attack. Experimental results obtained from different case studies demonstrate that the proposed homomorphic encryption-based privacy-preserving SIFT performs comparably to the original SIFT and that our method is useful in SIFT-based privacy-preserving applications.

All of the existing TV-point discrete fractional signal transforms require O(N2) computation complexity. In this paper, we propose a new discrete fractional signal transform whose computation complexity can be reduced to O(N1.5). This new transform is a fractional version of a DFT-based signal transform called as the Hirschman optimal transform (HOT) in the literature. Eigenvalues and eigenvectors properties of the HOT are also developed. Moreover, the proposed discrete fractional HOT transform is extended to further reduce the required computation complexity to linear order O(N). As an application example, we apply this new computationally efficient discrete fractional signal transform to encrypt digital images.

Non-uniform light distribution problems often arise in the text images taken by digital camera. In this paper, we propose a novel technique for text image uneven lighting removal using Empirical Mode Decomposition (EMD). The EMD is local, adaptive and useful for analyzing non-linear and non-stationary signals. In this method, we decompose images by EMD and get the background level locally and adaptively. This algorithm can enhance local contrast in the image while removing shadows for black-and-white text images. In addition, this work can be very helpful for text recognition. The experimental results show that the proposed approach can effectively enhance text images more readable under uneven lighting.

Compressive sensing (CS) has recently attracted much attention due to its unique feature of directly and simultaneously acquiring compressed and encrypted data based on their sparse or compressible properties. To securely transmit compressively sensed multimedia data over networks, it is required to support transcoder to securely convert compressed multimedia into several different types for diverse receivers. In this paper, a secure transcoding scheme for compressive multimedia sensing is proposed. We focus on securely converting compressively sensed multimedia data (not data compressed via standard codec) with a certain number of measurements into other different numbers of measurements without resorting to reconstruct the original data. We show that the security can be achieved via transforming multimedia re-sensing process into another secure domain at the transcoder. We also show that the computational security can be achieved while transmitting compressively sensed data between the sender (or each receiver) and the transcoder over networks.

As the Walsh (Hadamard) transform can be generalized into the Jacket transform, in this paper, we generalize the Haar transform into the Jacket-Haar transform. The entries of the Jacket-Haar transform are 0 and ±2k. Compared with the original Haar transform, the basis of the Jacket-Haar transform is general and more suitable for signal processing. Furthermore, with the proposed generalization algorithm, it is possible to define the N-point Jacket-Haar transform, where N is not a power of 2. From our simulations, the proposed Jacket Haar transform has better performance in ECG signal analysis.

In this paper, an improved method is proposed for the design of variable fractional-delay (VFD) IIR digital filters. The objective error function is constituted directly by the root-mean-squared error function of variable frequency response and the stability constrained function, so that the root-mean-squared error of variable frequency response can be minimized while the designed VFD IIR filter is stable. Several design examples will be presented to demonstrate the effectiveness of the proposed method.

Content-based image retrieval (CBIR) is an interesting but difficult topic of research. It uses the visual features to achieve the image searching on database. In this paper, we propose an image indexing for CBIR based on color feature, which consider both the computational complexity and the spatial relationship. We use a 3D mathematical model to design the color codebook and exploit the feature of the query image to adopt it. In the experiments, we discuss the three parameters affecting the performance and find out the corresponding optimal value to raise the retrieval speed and accuracy. Besides, we also demonstrate that the proposed scheme is robust for some image distortions and best matches human perception overall.

Video halftoning is a key technology for use in electronic paper (e-paper) or smart paper, which is an emerging display device that has received considerable attention recently. In this paper, a temporal frequency of flickering-distortion optimized video halftoning method is proposed. We first uncover three visual defects that conventional neighboring frame referencing-based video halftoning methods, due to their sequential changes of reference frames, will encounter. To deal with the problem, we then propose a reference frame update per GOP-based error diffusion video halftoning method based on a flickering sensitivity-based human visual model. To efficiently compromise between average temporal frequency of flickering (ATFoF) and visual quality, temporal frequency of flickering-distortion (TFoFD) is presented as a metric for video halftoning performance evaluation. Based on the proposed probability model of video halftoning, the TFoFD curve can be accurately estimated to optimize the tradeoff between quality and ATFoF before the video is halftoned. Our temporal frequency of flickering-distortion optimization strategy can also be applied to other video halftoning schemes for performance improvement. Experimental results and comparisons with known methods demonstrate the effectiveness of our video halftoning method.

Assessment of image similarity is fundamentally important to numerous multimedia applications. The goal of similarity assessment is to automatically assess the similarities among images in a perceptually consistent manner. In this paper, we interpret the image similarity assessment problem as an information fidelity problem. More specifically, we propose a feature-based approach to quantify the information that is present in a reference image and how much of this information can be extracted from a test image to assess the similarity between the two images. Here, we extract the feature points and their descriptors from an image, followed by learning the dictionary/basis for the descriptors in order to interpret the information present in this image. Then, we formulate the problem of the image similarity assessment in terms of sparse representation. To evaluate the applicability of the proposed feature-based sparse representation for image similarity assessment (FSRISA) technique, we apply FSRISA to three popular applications, namely, image copy detection, retrieval, and recognition by properly formulating them to sparse representation problems. Promising results have been obtained through simulations conducted on several public datasets, including the Stirmark benchmark, Corel-1000, COIL-20, COIL-100, and Caltech-101 datasets.

The S transform is a useful time-frequency analysis algorithm. Based on the concentration measure, a method to optimize the window width in the S transform has been proposed by previous studies along with some examples demonstrating its effectiveness. However, it is found that although this method performs well for the high and middle frequency signals, it may fail for the low frequency ones. In this paper, a new method, which is more flexible than the previous one, is proposed to deal with this problem. Comparison of these two methods for energy concentration enhancement is also provided. Experimental result shows that the proposed method achieves higher energy concentration in comparison to the previous one and the original ST.

Scale-invariant feature transform (SIFT) is a powerful tool extensively used in the community of pattern recognition and computer vision. The security issue of SIFT, however, is relatively unexplored. We point out the potential weakness of SIFT, meaning that the SIFT features can be deleted or destroyed while maintaining acceptable visual qualities. To properly achieve the tradeoff between security and robustness of SIFT, we present a cube-based secure transformation mechanism to enable the SIFT method to resist up to the chosen plaintext attack while robustness against geometric attacks can still be maintained. Security analysis and robustness verification are provided to demonstrate the effectiveness of the proposed (and modified) SIFT method.

Digital watermark is an important technology for the image verification. Many authors researching on color image watermarking opine RGB color space in the spatial domain is not suitable for embedding marks. In this paper, we propose a digital color image watermarking method using Singular Value Decomposition (SVD). The whole process including embedding and extracting could be finished in RGB components in spatial domain. Simulation results show that our method is successful in resolving the rightful ownership of the watermarked image with good robustness, good imperceptibility and higher security.

The IIR allpass fractional-delay fractional Hilbert transformer is designed in the complex-cepstrum domain. The maximal flatness criterion on the phase response is considered for the midband frequency. Two independent systems of linear equations are formulated, resulting in closed-form solutions of the even-index and odd-index parts of complex cepstrum of the denominator polynomial. Moreover, they are proportional to the two design parameters: fractional delay and phase shift. This is attractive in that a tunable scheme for variable parameters is realizable. Only two normalized complex-cepstrum sequences need to be designed, stored and tuned by scaling. Both nonre-cursive and recursive algorithms are available for renewing the filter coefficients from the complex cepstrum.

A new partially differential cepstrum is defined, which can be regarded as a new type of differential cepstrum. It saves half computational complexity compared with the previously defined differential cepstrum since only one dimension of partial derivative is considered. Nevertheless, this suffices for avoiding phase-unwrapping in complex-cepstrum calculation. As an application of complex cepstrum, we also introduce a windowing technique to construct the minimum-phase sequence from a mixed-phase one.

It is known that the 2-D DCT basis is complete and orthogonal in a rectangular region. In this paper, we introduce the way to generate the complete and orthogonal 2-D DCT basis in a trapezoid region or a triangular region without using the complicated Gram-Schmidt method. Moreover, since a polygon can be decomposed several triangular regions, the proposed method is also suitable for the polygonal region. Our algorithm can much generalize the JPEG algorithm. Instead of dividing an image into 8 by 8 blocks, we can divide an image into trapezoid or triangular regions and then transform and code each of them. In addition to the DCT basis, our method can also be used for generating the 2-D complete and orthogonal DFT basis, KLT basis, Legendre basis, Hadamard (Walsh) basis, and polynomial basis in the trapezoid and triangular regions.

This paper provides a novel method to obtain the eigenvectors of discrete Fourier transform (DFT), which are accurate approximations to the continuous Hermite-Gaussian functions (HGFs). The proposed method uses a generating matrix and an initial eigenvector. By multiplying the initial eigenvector with the generating matrix, we can derive a new eigenvector. Repeating this procedure we can acquire all the eigenvectors. Compare with the conventional O(N3) commutative matrix method, this new method can generate all the DFT eigenvectors with complexity reduced to O(N2logN). The generating matrix can be further used to intensify the conventional commuting matrix. The simulation result shows that the Hermite-Gaussian like (HGL) eigenvectors of the strengthened commuting matrix outperform those of Santhanam's.

In this paper, a music instrumentation analysis and identification method is proposed. In contrast to existing systems, it tries to identify the whole instrument set in polyphonic music and also decide whether each instrument actually dominates at a particular moment or not, but without calculating the exact pitch, onset timing, or the volume of each note. Moreover, it does not require the music source separation in advance. We address this problem by incorporating the beatsynchronous scheme with fuzzy clustering to analyze the instrument components. Experiments show that the instrument identification process results in an 85.19% averaging recognition rate, which is comparable with other existing systems. In addition, it generates the extra time-varying instrumentation information. This information can be considered as a new mid-level feature in music information retrieval systems.

The S transform is a useful linear time-frequency distribution and has been applied to various fields. Since the inverse S transform is an over-determined problem, there exist several different algorithms, which result in different filtering effects. This paper models the discrete S transform in matrix form and proposes a new inverse S transform algorithm with least square error in filters. This paper also compares the new inverse S transform with the previous ones.

Security is still a relatively unexplored issue in image hashing. In this paper, we address this problem and present a new metric, called minimum distortion estimation (MDE), by demonstrating its appropriateness over entropy for secure hashing evaluation. We investigate the relationship between bit changing rate and content distortion via statistical analyses of MDE. This provides a guideline for our design of a new secure image hashing method. The feasibility of our method is further demonstrated via comparisons with two known image hashing methods.

The integer color transform is a reversible operation that can transform one color coordinate into another one and both the inputs and the outputs are of integer forms. In this paper, we improve the integer color transforms derived in previous works. First, we relax the constraint that the scaling for each row should be the same. From this, the method of deriving the integer color transform becomes more flexible and we can derive the integer color transform with less implementation time and higher accuracy. Moreover, we use the new criterion, bit extension, to measure the performance of the integer color transform and propose a new way for accuracy analysis. With the proposed method, we derive the reversible integer RGB-to-YCbCr, KLA, XYZ, UVW, RcGcBc, and YUV transforms with even higher accuracy successfully.

Color quantization is a technique that reduces the number of distinct colors for a color image. It usually maps pixels of the color image to a small color palette. The display quality of the color-quantized image is taken most seriously. But in practical applications, we also need to consider the complexity of quantization algorithm and the storage of parameters. We develop a 3D mathematic model to design the color palette such that the above things are solved. We will show the proposed scheme is computationally inexpensive and the display quality of the color-quantized image tends to perform better as the codebook size increases, but the storage of total parameters does not increase. In addition, we also prove the color-mapped images generated can be used for the edge detection of color image.

A music similarity measure system based on the instrumentation information is proposed in this paper. We combine our previous instrumentation analysis algorithm with a newly designed similarity measure system, which aims at comparing songs solely on their instrumentation content. Several midlevel features are designed and integrated along with the existing low-level feature MFCCs. The weighted distance is then applied to rank the similarity of songs in pair inside the music database. We evaluate its performance by ten-fold cross validation on a Western classical music database. The objective test shows the incorporation of new mid-level features can increase the correctness of the composer classification task by approximately 10%.

Empirical mode decomposition (EMD) developed by Huang et al. is a nonlinear data analysis method for nonstationary real-valued time series. It has been applied extensively in many research areas. Recently, several generalized EMD methods for complex-valued data analysis was proposed. Since a plane closed curve comprises many two-dimensional (2D) space data points, one can imagine that the boundary points of a plane closed curve as a complex data sequence in the complex plane, and make use of the newly developed complex EMD (CEMD) to do further analysis. We have found that we can use CEMD to achieve boundary points noise-reduction of plane closed curves and perform shift-invariant, scale-invariant and rotation-invariant pattern recognition.

Different images have different amplitude spectrums. However, in this paper, with the proposed phase-key algorithm, we can make a series of images have the same amplitude spectrum but different phase key in the frequency domain. It is useful for image encryption, data compression, image transformation, and reducing the distortion in communication. Our algorithm can be applied for not only the FT but also all the operations with conjugate symmetric kernels. Moreover, we can also reverse the direction of the algorithm, i.e., make a series of images have the same phase spectrum and use the amplitude spectra to distinguish different images.

Scale-invariant feature transform (SIFT) is a powerful tool extensively used in the community of pattern recognition and computer vision. However, the security issue of SIFT is relatively unexplored in the literature. This paper investigates the potential weakness of SIFT, meaning that the SIFT features can be deleted or destroyed while maintaining acceptable visual qualities. We then propose an improved scheme to enhance the security of SIFT by introducing a key-based transform process to images. Experimental results demonstrate the effectiveness of our methods.

In this letter, a new commuting matrix with random discrete Fourier transform (DFT) eigenvectors is first constructed. A random discrete fractional Fourier transform (RDFRFT) kernel matrix with random DFT eigenvectors and eigenvalues is then proposed. The RDFRFT has an important feature that the magnitude and phase of its transform output are both random. As an application example, a security-enhanced image encryption scheme based on the RDFRFT is illustrated.

Recently, Candan introduced higher order DFT-commuting matrices whose eigenvectors are accurate approximations to the continuous Hermite-Gaussian functions (HGFs). However, the highest order 2k of the O(h2k) N×N DFT-commuting matrices proposed by Candan is restricted by 2k+1≤N. In this paper, we remove that restriction of order upper bound by developing a coefficient truncation technique to construct arbitrary-order DFT-commuting matrices. Exploiting that coefficient truncation technique, we also develop a method to construct n-diagonal arbitrary-order DFT-commuting matrices, whose number of nonzero diagonal bands n can be prespecified at will. Results of computer experiments show that the Hermite-Gaussian-like (HGL) eigenvectors of the new DFT-commuting matrices proposed in this paper outperform those of Candan’s.

Palette re-indexing has been shown to be an effective way to improve the compression of color-indexed images. Based on two operations, i.e., sampling and swapping, we propose a novel re-indexing technique with the lowest complexity on the palette size and ability to further improve existing methods, which are two unique features that contrast others. Experiment results verify the effectiveness of this technique.

Video halftoning is a key technology for use in the innovative display - electronic paper (e-paper). Since e-paper is power-limited, halftone video compression becomes an emerging issue but is still relatively unexplored. In this paper, this issue is addressed and a novel halftone video compression scheme is proposed. Our scheme is mainly composed of three components: block decomposition, block-based halftone quantization, and source coding. We evaluate the proposed method via lossless halftone video compression comparison with the famous standard, JBIG2. In addition, we demonstrate the rate-distortion performance of the proposed lossy halftone video compression method.

Video halftoning is a key technology for use in the new display device, electronic paper (e-paper). One challenging issue is how to save the limited power of mobile e-paper device when a halftone video is displayed with various frame rates. In this paper, we propose a power-scalable multi-layer halftone video display scheme, which is composed of layer coding, non-uniform sampling, and flicker rate reduction. Our method not only efficiently save power over the state of the art video halftoning technology but also keep the quality of halftone video nearly unchanged when power saving is additionally considered. Experimental results demonstrate the effectiveness of the proposed method.

We propose a design of discrete Fractional Hilbert transformer. Through the time domain analysis of the ideal input and output signal of a LTI system, we derived equations which can be solved numerically for the filter’s impulse response. The conventional Hilbert transformer is derived as a special case of the fractional Hilbert transformer. We also show that the difference between the designed system and the ideal system can be represented by the Peano kernel of the system. Some designing examples of the proposed filter are also illustrated.

This paper proposes a novel automatic video diagnosing method. The purpose of this study is to detect the attack added on the authorized video and identify the attack category. The video is added with the crypto-watermarks using dual-domain quaternary watermarking algorithm in advance. The crypto-watermarks, which are generated using visual cryptography, have different capabilities against the various attacks. We extract the watermarks from the suspected video, measure the bit-error-rate between the extracted and specified crypto-watermarks, and then analyze bit-error-rates to determine what kind of attack added on the video. The experimental results demonstrate that the proposed method not only can identify the single attack, but it can identify the composite attack and detect the corrupted frames. Even if the video is not embedded with crypto-watermarks, we can differentiate it from the authorized videos.

In this letter, an iterative weighted least-squares (LS) approach is proposed for the design of variable fractional-delay (VFD) finite impulse response (FIR) digital filters in minimax sense. For deriving the elements of relevant matrices, there is no need for numerical integration or closed-form formulation and they obey given specifications. Comparing with the existing method, the proposed method does not lead to a misleading problem, and the performance of convergence is also better. Especially, it is found that the used LS weighting function is only dependent on the frequency, not on the tunable parameter, which makes it easier for the minimax design of VFD FIR digital filters.

Traditional approaches to receiver-driven layered multicast apply coarse-grain layered congestion control, which enables each receiver to adjust its receiving rate to match the available bandwidth. However, this restricts the scalability of fine-grain scalable video coding. In this paper, we present an approach that facilitates bandwidth inference congestion control in a hybrid coarse/fine layered multicast scheme for multimedia delivery. One-way delay trend detection has proven effective in explicitly or implicitly estimating end-to-end available bandwidth. Using a hierarchical layered probing scheme and a delay trend detection method, we have developed a congestion control protocol for fine-grain layered multicast. Combining this protocol with scalable video coding, we present a framework that achieves efficient scalable video streaming over heterogeneous networks. The performance of our hybrid coarse/fine layered multicast scheme is evaluated by network simulations and the video coding efficiency.

In this paper, we present two novel robust methods for embedding watermarks into dithered halftone images. The first method is named Paired Subimage Matching Ordered Dithering (PSMOD), of which the decoder is provided with a priori information of the original watermark, and the corresponding application is copyright protection. The other method, Blind Paired Subimage Matching Ordered Dithering (BPSMOD), does not require the knowledge of the original watermark, and the main application is secret communication. Both methods utilize the bit and sub-subimage interleaving preprocesses. The experiments show that both techniques are sufficiently robust to guard against the cropping, tampering, and print-and-scan degradation processes, in either B/W or color dithered images. Both techniques are also sufficiently flexible for various levels of embedded capacities. Furthermore, a novel progressive coding scheme is also presented in this paper for the efficient display of dithered images. After the preprocessing of bit-interleaving, this algorithm utilizes the characteristic of reordered image to determine the transmitting order and then progressively reconstructs the dithered image. Moreover, the dithered images are further compressed by lossy and lossless procedures. The experimental results demonstrate high-quality reconstructions while maintaining low transmitted bit rates.

The S transform is a powerful linear time-frequency representation, and it is especially useful for filter in the time-frequency spectrum. To improve the time resolution of the filter applications, Schimmel and Gallart have proposed a new method for inverse S transform. This new method performs much better than the original in time localization with time-frequency filters. However, there exists some distortion of the inverse transformed signal that it will be enhanced in the positive but suppressed in the negative frequency part. In this paper we will demonstrate the distortion and propose a modified method to derive the correct inverse transformed signal and provide satisfactory time localization in filtering.

A more accurate algorithm for corner and edge detections that is the improved form of the well-known Harris' algorithm is introduced. First, instead of approximating |L[m+x, n+y]-L[m, n]|2just in terms of x2, xy, and y2, we will approximate |L[m+x, n+y]-L[m, n]|(L[m+x, n+y]-L[m, n]) by the linear combination of x2, xy, y2, x, y, and 1. With the modifications, we can observe the sign of variation. It can avoid misjudging the pixel at a dot or on a ridge as a corner and is also helpful for increasing the robustness to noise. Moreover, we also use orthogonal polynomial expansion and table looking up and define the comity as the "integration" of the quadratic function to further improve the performance. From simulations, our algorithm can much reduce the probability of regarding a non-corner pixel as a corner. In addition, our algorithm is also effective for edge detection.

This paper presents a method to localize and to recover the tampered areas in the watermarked image simultaneously. First, the proposed watermarking algorithm aims to embed a bi-watermark, which is the binary halftone of the downscaled host image, into the host image. While the watermarked image is tampered unauthorizedly, the extracted bi-watermark can be exploited to localize the tampered areas automatically without initial bi-watermark. Subsequently, Gaussian lowpass filter and quadratic programming are used to restore the bi-watermark to gray-scale image for inverse halftoning procedure. Eventually, the restored gray-scale image is used to recover the tampered areas.

Video halftoning is a key technology for use in the new display device, electronic paper (e-paper). This is still a rather unexplored field. The challenging issue of video halftoning is the elimination of flicker flaw that will appear due to error diffusion in the temporal domain. In this paper, we propose a new video halftoning method, which is composed of spatial error diffusion and inter-frame reference error diffusion. In addition, since our method can efficiently reduce the flicker flaws, another advantage is that the halftone video sequence can be efficiently compressed. When compared with traditional 2D and 3D error diffusion techniques, experimental results show that our method can significantly reduce the average flicker rates.

A 2.5-domain tri-watermarking algorithm (2.5D-TW) is presented in this paper. The proposed algorithm is the integration of dual domain bi-watermarking algorithm and visual cryptography, and the embedded tri-watermark is composed of three binary watermarks. The tri-watermark is embedded into the encoded blocks in discrete cosine transform (DCT) domain, however, the tri-watermark can be extracted from the DCT blocks and the decoded frames in spatial domain. Moreover, two types of third binary watermark of the tri-watermark are developed namely the intra-watermark and inter-watermark, those binary watermarks reveal the different robustness against various attacks. The proposed method attempts to localize the tampered areas and to detect the temporal attack.

In this paper, we generalize the lifting scheme and the triangular matrix scheme. For the existing lifting scheme and the triangular matrix scheme, the entries on the diagonal line must be 1 or 2k. In this paper, we find that this constraint can be relaxed and the lifting or the triangular matrix is still reversible. Thus, the constraint that det(A) = 2Lis not required and we can convert a matrix into a reversible integer transform without pre-scaling even when det(A) ne 2L. Moreover, the proposed scaled schemes are also helpful for improving the accuracy and reducing the implementation complexity.

The paper describes a cepstrum-based approach to design the maximally flat allpass fractional delay filter and the fractional Hilbert transformers. The maximal flatness criteria on the phase/group delay responses are formulated as a system of linear equations in terms of cepstral coefficients. The solution to the cepstral coefficients has closed-form expression. Moreover, it's very attractive that the resultant cepstral coefficients are directly proportional to the design parameters: the fractional delay and phase shift in the delay filters and Hilbert transformers, respectively. This virtue implies a simple scheme for updating new filter coefficients corresponding to various delay value or phase shift amount. Only one set of cepstral coefficients needs to be designed and stored and the new set is obtained simply by multiplying the old set with a ratio. A fixed module is used to update the filter coefficients from the cepstral coefficients.

A special class of odd-symmetric length-4N periodic signals is studied, and it is shown how the odd Ramanujan sums are used as weighting coefficients to compute their pure imaginary discrete Fourier transform (DFT) integer-valued coefficients. The odd Ramanujan sum, being the sums of complex roots of unity, can be calculated either using closed-form formulas or computed recursively through the impulse response of a derived infinite impulse response (IIR) filter. This special class of odd-symmetric signals and odd Ramanujan sums can be combined together with the previous even-symmetric special class signals and the well-known even Ramanujan sums as a useful tool for signal processing

In this paper, we propose a systematic approach that approximates a target dictionary to reduce the complexity of a matching pursuit encoder. We combine calculation of the inner products and maximum atom extraction of a matching pursuit video coding scheme based on eigendictionary approximation and tree-based vector quantization. The approach makes the codec design and optimization cleaner and more systematic than previous dictionary approximation methods. We vary the quality of approximation to demonstrate the tradeoff between computational complexity and coding efficiency. The experiment results show that our codec achieves speed-up factors of up to 100 with a performance loss of less than 0.1 dB. We use double-stimulus impairment scale scores to evaluate the perceptual quality of our approach for different levels of complexity.

In this correspondence, we introduce a systematic algorithm that can convert any 3 x 3 color transform into a reversible integer-to-integer transform. We also discuss the ways to improve accuracy and reduce implementation complexity. We derive the integer RGB-to-KLA, IV1 V2, YCbCr, DCT, YUV, and YIQ transforms that are optimal in accuracy.

This correspondence presents new rate-1 space-time block codes (STBCs) attending full diversity over every quadrature amplitude modulation (QAM) constellation when the number of Tx antennas is a power of two. From the simulation results, our design performs very closely to the quasi-orthogonal code with constellation rotation over 4-QAM and 16-QAM in the case of four Tx antennas over quasi-static Rayleigh fading channels. Moreover, the proposed codes would not cause any constellation expansion over QAM symbols in contrast with the quasi-orthogonal codes with constellation rotations

We propose a novel semi-fragile multiple-watermarking algorithm based on quantization index modulation. This algorithm utilizes two quantization steps to yield the non-uniform intervals in the real-number axis. Each interval corresponds to one binary symbol, includes stable-zero (S0), unstable-zero (U0), stable-one (S1), and unstable-one (U1). In addition, visual cryptography is integrated with the watermarking algorithm to increase the watermark capacity. Therefore, the host image is embedded the multiple watermarks, and then we extract the watermarks from the corrupted image. According to the extracted watermarks, the algorithm achieves the tamper proofing and attack identification. From the experimental result, it shows single and multiple tampered areas are detected and demonstrates that the amount of test images will not influence the accuracy of attack identification.

In this paper, we discuss the relations among the random process, the Wigner distribution function, the ambiguity function, and the fractional Fourier transform (FRFT). We find many interesting properties. For example, if we do the FRFT for a stationary process, although the result in no longer stationary, the amplitude of its covariance function is still independent of time. Moreover, for the FRFT of a stationary random process, the ambiguity function will be a radiant line passing through (0, 0) and the Wigner distribution function will be invariant along a certain direction. We also define the fractional stationary random process and find that a non-stationary random process can be expressed a summation of fractional stationary random processes. The proposed theorems will be useful for filter design, noise synthesis and analysis, system modeling, and communication.

The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this paper, we extend the DFRFT to have N order parameters, where N is the number of the input data points. The proposed multiple-parameter discrete fractional Fourier transform (MPDFRFT) is shown to have all of the desired properties for fractional transforms. In fact, the MPDFRFT reduces to the DFRFT when all of its order parameters are the same. To show an application example of the MPDFRFT, we exploit its multiple-parameter feature and propose the double random phase encoding in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme in the MPDFRFT domain significantly enhances data security.

This paper presents a modified approach to the successive mean quantization transform, which is called as the weighted histogram separation (WHS) for enhancement of color images. Property of WHS situates between the successive mean quantization transform and the histogram equalization. In addition, this approach is further applied to the local enhancement, which is similar to the adaptive histogram equalization, and it is termed as the adaptive weighted histogram separation (AWHS). A comparison with successive mean quantization transform and histogram equalization has been performed in the experiments.

A dual-domain bi-watermarking algorithm is proposed in this paper. This algorithm embeds bi-watermark in DCT domain, but bi-watermark can be extracted in both spatial and DCT domains. Therefore, it can implement on the DCT-based compressed image/frame. The dual-domain bi-watermarking algorithm is the extension of the spatial-domain bi-watermarking algorithm, which implements quantization index modulation with two quantization step sizes. These quantization step sizes construct the non-uniform quantization intervals. Additionally, the luminance quantization table of JPEG compression is considered in the algorithm. In the experimental result, two extracted watermarks show the capability for various compression rates, and the watermarks also reveal the different robustness against the global and the regional attacks.

Video coding schemes based on matching pursuits have been shown to have better coding efficiency and perceptual quality at low bit rates than DCT-based video coding schemes. Matching pursuit is a greedy algorithm that decomposes a signal into a linear combination of bases within an over complete dictionary. However, as the bases are not independent, the redundancy in linear combinations increases as the number of iterations of matching pursuit increases. In this paper, we introduce an orthonormal matching pursuit algorithm that reduces the redundancy between bases and represents a signal by a linear combination of bases more efficiently. Our proposed updated full search matching pursuit algorithm has been shown to be effective in both coding performance and computational complexity. Based on this algorithm, we present an orthonormal matching pursuit video coding scheme that achieves a more efficient coding performance. The coding efficiency and perceptual quality are evaluated and compared to traditional matching pursuit video coding schemes.

Integer transform are the discrete transforms whose entries are summations of 2/sup -k/. If for an integer transform, we can perfectly recover the input from the output, we call it the reversible integer transform. In 2001, Hao and Shi developed an algorithm that can convert any reversible non-integer transform into a reversible integer transform. In this paper, we improve their works. First, we simplify the way of derivation. Then, we analyze the approximation error and introduce the way to reduce it. We also discuss the problem of bit constraint and how to reduce the number of time cycle in implementation.

8 types of maximally flat FIR fractional delay filters are proposed. They are designed by separately approximating the real part and the imaginary part of the frequency response. Among these 8 types of filters, two of them are equivalent to the existing design results in the open literature (Samadi, 2004). Therefore, a more general closed-form design of the maximally flat FIR fractional delay filters is described in this paper and some design examples of FIR fractional delay filters are illustrated.

The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this letter, we extend the DFRFT to have N order parameters, where N is the number of the input data points. The proposed multiple-parameter discrete fractional Fourier transform (MPDFRFT) is shown to have all of the desired properties for fractional transforms. In fact, the MPDFRFT reduces to the DFRFT when all of its order parameters are the same. To show an application example of the MPDFRFT, we exploit its multiple-parameter feature and propose the double random phase encoding in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme in the MPDFRFT domain significantly enhances data security.

The three-dimensional (3-D) Fourier transform of the nonaccelerating object in an image sequence lies on a plane passing through the origin of the 3-D frequency domain. Instead of using a 3-D frequency planar filter, we propose a new filter design technique for object tracking using a one-dimensional trajectory filter-in the spatiotemporal domain. This filter can track a moving object with linear or nonlinear trajectory without prior knowledge of the target trajectory. Also, it is easy to design and has a very low computational complexity. More importantly, it can be implemented in real time.

Eight types of maximally flat finite impulse response (FIR) fractional delay filters are proposed. They are designed by separately approximating the real part and the imaginary part of the frequency response. Among these eight types of filters, two of them are equivalent to the existing design results in the open literature. Therefore, a more general closed-form design of the maximally flat FIR fractional delay filters is described in this letter, and some design examples of FIR fractional delay filters will be illustrated.

Matching pursuit (MP) is a greedy algorithm that decomposes a signal into a linear combination of bases within an over-complete dictionary. The MP algorithm is usually only approximated due to its massive computational complexity. By approximating a residual in a subspace, we propose a multiple blocks MP update algorithm for video coding that achieves a faster and better MP approximation than traditional algorithms. As the subspace is dependent on a residual, our algorithm is content-dependent. We evaluate the coding performance, including the peak signal-to-noise ratio, runtime, and subjective quality, of our algorithm and compare it with traditional MP algorithms.

This paper presents a novel approach for improving the robustness of the quantization-based watermarking scheme. Unlike the conventional approach, which quantizes the host value to the center of the objective interval, the proposed scheme offers the flexibility of determining the quantized value. Given tolerable embedding-induced distortion and the host value, the quantized value can be analytically determined in a closed-form solution, instead of being fixed at the center of the interval. To objectively compare the robustness, different watermarking schemes are implemented in the same distortion-to-noise ratio (DNR) scenario and then the probabilities of error detection are measured. Simulation results indicate that the proposed scheme, compared to the conventional quantization watermarking, could reduce the error probability by 0.113 when DNR is set to 0 dB, whereas the reduction is only 0.037 for the recent Wu's approach. Furthermore, without the finite possible values of the watermarked data, the proposed scheme provides sufficient nondisclosure for the quantization step, whereas in the conventional quantization-based watermarking, the quantization step can be easily inferred from the watermarked data

A novel image recovery algorithm for removing visible watermarks is presented. Independent component analysis (ICA) is utilized to separate source images from watermarked and reference images. Three independent component analysis approaches are examined in the proposed algorithm, which includes joint approximate diagonalization of eigenmatrices, second-order blind identification, and FastICA. Moreover, five different visible watermarking methods to embed uniform and linear-gradient watermarks are implemented. The experimental results show that visible watermarks are successfully removed, and that the proposed algorithm is independent of both the adopted ICA approach and the visible watermarking method. In the final experiment, several public domain images sourced from various websites are tested. The results of this study demonstrate that the proposed algorithm can blindly and successfully remove the visible watermarks without knowing the watermarking methods in advance

The process of limited-color image compression usually involves color quantization followed by palette re-indexing. Palette re-indexing could improve the compression of color-indexed images, but it is still complicated and consumes extra time. Making use of the topology-preserving property of self-organizing Kohonen feature map, we can generate a fairly good color index table to achieve both high image quality and high compression, without re-indexing. Promising experiment results will be presented.

In this paper, a high-capacity data hiding is proposed for embedding a large amount of information into halftone images. The embedded watermark can be distributed into several error-diffused images with the proposed minimal-error bit-searching technique (MEBS). The method can also be generalized to self-decoding mode with dot diffusion or color halftone images. From the experiments, the embedded capacity from 33% up to 50% and good quality results are achieved. Furthermore, the proposed MEBS method is also extended for robust watermarking against the degradation from printing-and-scanning and several kinds of distortions. Finally, a least-mean square-based halftoning is developed to produce an edge-enhanced halftone image, and the technique also cooperates with MEBS for all the applications described above, including high-capacity data hiding with secret sharing or self-decoding mode, as well as robust watermarking. The results prove much sharper than the error diffusion or dot diffusion methods.

It is known that one can use Shannon's theory to sample a bandlimited signal. In this paper, we introduce how to use prolate spheroidal wave functions (PSWFs) to sample a time-limited and nearly band-limited signal. PSWFs have the property of optimal energy concentration. Thus we can apply it to sampling theory to reduce the aliasing error of the recovered signal. We derive a theory that can estimate the upper bound of the error. With it, we can determine, to achieve certain accuracy, how many samples we should acquire. Moreover, we combine the proposed sampling theory with the fractional Fourier transform (FRFT). We also find an important theory, i.e., to achieve a certain degree of accuracy, the number of sampling points required for a signal is proportional to the 'area' of its time-frequency distribution.

A halftone watermarking technique of high capacity, robustness, and capacity flexibility is presented in this paper. This parity-matched error diffusion (PMEDF) method is capable of achieving an embedded capacity as high as 6.25% to 25% with good image quality and without the original image as the reference to decode the watermark. As the experimental results demonstrated, this technique is able to guard against degradation due to cropping, tampering, and printed-and-scanned process in error-diffused halftone images.

Based on discrete Hermite-Gaussian like functions, a discrete fractional Fourier transform (DFRFT) which provides sample approximations of the continuous fractional Fourier transform was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be better discrete Hermite-Gaussian like functions than those developed before. Furthermore, by appropriately combining two linearly independent matrices which both commute with the DFT matrix, we develop a method to obtain even better discrete Hermite-Gaussian like functions. Then, new versions of DFRFT produce their transform outputs more close to the samples of the continuous fractional Fourier transform, and their application is illustrated.

It has been shown that a complex orthogonal design that provides full diversity and full transmission rate is not possible for more than two transmit antennas. The paper presents a new class of quasi-orthogonal space-time block codes using a group-theoretic method. The new designs can achieve full diversity for quadrature phase-shift-keying modulation, like the system using rotated constellations. Based upon the analysis of the new codes, a relaxed designing viewpoint for full diversity is proposed for arbitrary signal constellations.

Matching pursuit (MP) video coding has been demonstrated to attain a better coding performance than DCT-based video coding in terms of PSNR and perceptual quality at very low bit rates. However, because of its massive computational complexity, the MP algorithm is usually only approximated. By approximating a residual in a subspace, we propose a multiple blocks search and update algorithm in MP video coding to achieve a faster and better MP approximation. In this paper, we evaluate the performance and compare it to the traditional one-block search algorithms. The experimental results show that our proposed algorithm can significantly improve the coding performance and encoding time.

In this paper, we introduce a new algorithm for corner detection. Instead of calculating the gradients along x and y-axes, which is the common step of many existed algorithms, we use the sum of differences to observe the variations along the adaptive vertical and tangent axes. We classify the variations into 36 types and use the 'case table' to determine whether a pixel is a corner. We do some experiments and show that our algorithm can detect almost all the corners of a complicated natural image (such as Lena image and Fruit image) successfully. In addition to corner detection, it is also possible to use our algorithm to detect the edges, ridges, valleys, isolated dots, saddles, and plain regions of a natural image.

In color image processing, the RGB color coordinate is usually transformed into another one (e.g., YIQ or KLA) for system fitting or other purposes. Most of the color transforms are done by 3/spl times/3 matrices. However, these matrices are always not fixed-point. In this paper, we use a systematic algorithm to convert every 3/spl times/3 color transform into a reversible integer-to-integer transform. The resulted transform can be implemented with only fixed-point processor and no floating-point processor is required. Moreover, with the use of ladder-truncation technique, we can make least bit of the output the same as that of the input, and the long bit-length problem that always occurs for other integer transforms can be avoided. We derive the integer color transforms of RGB-to-KLA, IV/sub 1/V/sub 2/, YCrCb, DCT, and YIQ successfully.

This article presents a set of quasi-orthogonal spacetime block codes for four transmit antennas that achieves full diversity and high coding gain whenever a square lattice constellation is adopted. From the simulation results, the new designs perform very closely to quasi-orthogonal codes with constellation rotations. Without a search of the optimal rotation angle and any constellation expansion, our new codes yield an advantageous transmission scheme for QPSK and 16-QAM modulations.

In this letter, we present a novel robust method for embedding watermarks into dithered halftone images. The method is named paired sub-image matching ordered dithering (PSMOD), of which the decoder is provided with a priori information of the original watermark. The method utilizes the bit and sub-subimage interleaving preprocesses. The experiments show that the technique is sufficiently robust to guard against the cropping, tampering, and printed-and-scanned degradation processes, in either B/W or color dithered images. This technique is also sufficiently flexible for various levels of embedded capacities.

An efficient method for computing a length-N Discrete Cosine Transform (DCT) from three consecutive length-N/3 DCTs is proposed. This method differs from previous ones in that it reduces considerable 31-38% arithmetic operations and uses only length-N/3 DCTs instead of length-N DCTs. We also find its great applications in fractional scaling of a block DCT-based image by the factor of 1/2/sup /spl alpha//3/sup /spl beta//. This would be very useful in high-definition television (HDTV) standard, whose display size is usually 16:9. The comparison with conventional methods is provided.

Most of the existing methods designed to implement fractional interpolation and decimation are limited by rational scaling factors such as L/M, where L and M are positive integers. The general procedure is usually done with up-sampling by L first, and then followed by down-sampling by M. This scheme, however, requires two steps and higher sampling rates to fulfill and is not capable in dealing with irrational scaling factors, which cannot be represented by L/M. We propose a new method to solve the above two difficulties by a single step. Furthermore, a new structure of a two-channel nonuniform perfect reconstruction filter bank is derived using this new method, and the experimental results are presented.

The design potential of using quaternionic numbers to identify a 4/spl times/4 real orthogonal space-time block code has been exploited in various communication articles. Although it has been shown that orthogonal codes in full-rate exist only for 2 Tx-antennas in complex constellations, a series of complex quasi-orthogonal codes for 4 Tx-antennas is still proposed to have good performance recently. This quasi-orthogonal scheme enables the codes to reach the optimal nonorthogonality, which can be measured by taking the expectation over all transmit signals of the ratios between the powers of the off-diagonal and diagonal components. This correspondence extends the quaternionic identification to the above encoding methods. Based upon tensor product for giving the quaternionic space a linear extension, a complete necessary and sufficient condition for identifying any given complex quasi-orthogonal code with the extended space is generalized by considering every possible two-dimensional R-algebra.

For an MPEG coding scheme, the encoder can do more than video compression. In this paper, a novel MPEG codec embedded with scene-effect information detection and insertion is proposed to provide more functionality at the decoder end. Based on the macroblock (MB) type of information that is generated simultaneously in the encoding process, a single-pass automatic scene-effect insertion MPEG coding scheme can be achieved. Using the USER/spl I.bar/DATA of picture header, the video output bitstreams by our method still conform to the conventional MPEG decoding system. The proposed method provides a solution toward upgrading the existing MPEG codec with low complexity to accomplish at least two major advantages. Precise and effective video browsing resulting from the scene-effect extraction can significantly reduce the user's time to look up what they are interested in. For video transmission, the bitstreams containing scene-effect information can obtain better error concealment performance when scene changes are involved. Compared with the gain it achieves, the payout of our algorithm is very worthy with comparatively small efforts.

We propose a new systematic approach to reduce matching pursuit (MP) encoder complexity. MP codecs are asymmetric as decoder complexity is low while the encoder complexity is extremely high. An MP encoder contains three components: the inner products, maximum atom extraction and atom encoding. We propose a new approach which combines the first two components using eigen-dictionary approximation and tree-based vector quantization (VQ). The advantages of this are a simpler design and a slower growth of computational costs as the target dictionary becomes large than traditional approaches. By varying the approximation accuracy, our algorithm can provide the trade-off between coding performance and speed-up of the MP encoder.

In this paper, a high capacity data hiding is proposed for embedding a large amount of information into halftone images. The embedded watermark can be distributed into several error-diffused images by the proposed minimal error bit searching technique (MEBS). The method can be generalized to self-decoding mode with dot diffusion or color halftone images. From the experiments, the embedded capacity from 33% up to 50% and good quality result are achieved. Furthermore, the proposed MEBS method is also extended for robust watermarking to against the degradation from printing-and-scanning and several kinds of distortions.

An efficient method for computing a length-N DCT given three consecutive length-N/3 DCTs is proposed. This method differs from previous ones in that it reduces considerable arithmetic operations and uses only length-N/3 DCTs instead of length-N DCTs. We also find its great applications in fractional scaling of a DCT-based image by the factor of N/2/sup /spl alpha//3/sup /spl beta//. This would be very useful in HDTV standard, whose display size is usually 16:9. The comparison with conventional methods is provided in this paper.

News, magazines, Web pages, etc. in modern life always contain much text information. We propose a novel approach to detect text in images with very low false alarm rate. First of all, neural network color quantization is used to compact text color. Second, 3D histogram analysis chooses several color candidates, and then extracts each of these color candidates to obtain several bi-level images. Moreover, for each bi-level image, connectivity analysis and some morphological operators are fed to produce character candidates. Furthermore, we calculate some spatial features and relationships of each text candidate. Finally, we can localize text regions by authentication from LOG (Laplacian of Gaussian) edge detector. Meanwhile, in complex color images, multi-quantization layers can be integrated to reject non-text parts and reduce false alarm rate.

This letter presents an efficient split vector-radix-2/8 fast Fourier transform (FFT) algorithm. The split vector-radix-2/8 FFT algorithm saves 14% real multiplications and has much lower arithmetic complexity than the split vector-radix-2/4 FFT algorithm. Moreover, this algorithm reduces 25% data loads and stores compared with the split vector-radix-2/4 FFT algorithm.

In this letter, we propose a novel all-pass (AP) fractional delay filter whose denominator polynomial is obtained by truncating the power series of a certain function. This function is derived from the frequency response of the denominator whose magnitude response is related to the desired phase response through the Hilbert transform since the denominator of a stable AP filter is of minimum phase. The target function and corresponding power series are calculated analytically and expressed in closed form. The closed-form expressions facilitate the analysis of stability. According to the properties for the coefficients of the denominator polynomial, we show that the proposed AP filter is stable for positive delay. Numerical examples indicate that the phase delays of the proposed filters are flat around DC.

This work presents a novel algorithm using color contrast enhancement and lacuna texture synthesis is proposed for the virtual restoration of ancient Chinese paintings. Color contrast enhancement based on saturation and de-saturation is performed in the u'v'Y color space, to change the saturation value in the chromaticity diagram, and adaptive histogram equalization then is adopted to adjust the luminance component. Additionally, this work presents a new patching method using the Markov Random Field (MRF) model of texture synthesis. Eliminating undesirable aged painting patterns, such as stains, crevices, and artifacts, and then filling the lacuna regions with the appropriate textures is simple and efficient. The synthesization procedure integrates three key approaches, weighted mask, annular scan and auxiliary, with neighborhood searching. These approaches can maintain a complete shape and prevent edge disconnection in the final results. Moreover, the boundary between original and synthesized paintings is seamless, and unable to distinguish in which the undesirable pattern appears.

In this paper, the impact of scene change on the conventional error concealment method is addressed and a novel error concealment method is proposed to improve the insufficiency of the conventional temporal error concealment algorithm due to the occurrence of scene change. Combining with the low complexity scene change detection algorithm using macroblock type information, the corrupt blocks resulting from bit errors are concealed either temporally or spatially depending on whether or not an abrupt scene change is found. In the case of gradual scene change, a novel error concealment method of interpolation and extrapolation is proposed to utilize the linear property of gradual scene change sequence, and effectively reduce the concealment error in comparison with the conventional algorithm. A great improvement of about 3 to 5 dB PSNR on average and 6 to 8 dB in some cases is obtained with very little memory and computation overhead.

It is well-known that the Hilbert transform (HLT) is useful for generating analytic signals, and saving the bandwidth required, in communication. However, it is less known that the HLT is also a useful tool for edge detection. We introduce the generalized radiant Hilbert transform (GRHLT), and illustrate how to use it for edge detection. The GRHLT is the general form of the two-dimensional HLT. Together with some other techniques (such as section dividing and shorter impulse response modification), we can use the GRHLT to detect the edges of images exactly. The GRHLT used for edge detection has a higher capability for noise immunity than other edge detection algorithms. Besides, we can also use the GRHLT for directional edge detection, i.e., detecting edges with certain directions.

In this paper, we first discuss the singular value decomposition (SVD) of a quaternion matrix and propose an algorithm to calculate the SVD of a quaternion matrix using its equivalent complex matrix. The singular values of a quaternion matrix are still real and positive, but the two unitary matrices are quaternion matrices with quaternion entries. Then, applications for color image processing by the SVD of a quaternion matrix are given. Since a quaternion matrix can represent a color image, so we can use the SVD of a quaternion matrix to decompose a color image. Therefore, many useful image processing methods by SVD, such as eigen-images, image compression, image enhancement and denoise, can be extended to color image processing without separating the color image into three channel images.

In this letter, we propose a low-complexity algorithm for embedding watermarks into two or more error-diffused images. The first one is only a regular error-diffused image, and the others are achieved by applying the proposed noise-balanced error diffusion technique (NBEDF) to the original gray-level image. The visual decoding pattern can be perceived when these two or more similar error-diffused images are overlaid each other. Furthermore, with the proposed modified version of NBEDF, the two halftone images can be made from two totally different gray-tone images and still provide a clear and sharp visual decoding pattern.

In this paper, the Taylor series expansion is used to transform the design problem of a fractional delay filter into the one of a first-order differentiator such that the conventional finite-impulse response and infinite-impulse response differentiators can be applied to design a fractional delay filter directly. The proposed structure is more efficient than the well-known Farrow structure in terms of filter coefficient storage because only one first-order differentiator needs to be designed and implemented. Moreover, one design example is demonstrated to illustrate the effectiveness of this new design approach.

A low computational complexity noise-balanced error diffusion (NBEDF) technique is proposed for embedding watermarks into error-diffused images. The visual decoding pattern can be perceived when two or more similar NBEDF images are overlaid, even in a high activity region. Also, with the modified improved version of NBEDF, two halftone images can be made from two totally different gray-tone images, and still provide a clear and sharp visual decoding pattern. With self-decoding techniques, we can also decode the pattern with only one NBEDF image. However, the NBEDF method is not so robust to damage due to printing or other distortions. Thus, a kernels-alternated error diffusion (KAEDF) technique is proposed. By using them alternately in the halftone process, we find that two well-known kernels (Jarvis, J.F. et al., 1976; Stucki, P., 1981) are compatible. In the decoder, because the spectral distributions of Jarvis and Stucki kernels are different in the 2D fast Fourier transform domain, we use the cumulative squared Euclidean distance criterion to determine each cell in a watermarked halftone image belonging to either Jarvis or Stucki, and then decode the watermark. Furthermore, because the detailed textures of Jarvis and Stucki patterns are somewhat different in the spatial domain, the lookup table (LUT) technique is also used for fast decoding. From simulation results, the correct decoding rates for both techniques are high and extremely robust, even after printing and scanning processes. Finally, we extend the hybrid NBEDF and KAEDF algorithms to two color EDF halftone images, where 8 independent KAEDF watermarks and 16 NBEDF watermarks can be inserted and still achieve a high-quality result.

We propose an effective color filter array (CFA) interpolation method for digital still cameras (DSCs) using a simple image model that correlates the R,G,B channels. In this model, we define the constants K/sub R/ as green minus red and K/sub B/ as green minus blue. For real-world images, the contrasts of K/sub R/ and K/sub B/ are quite flat over a small region and this property is suitable for interpolation. The main contribution of this paper is that we propose a low-complexity interpolation method to improve the image quality. We show that the frequency response of the proposed method is better than the conventional methods. Simulation results also verify that the proposed method obtain superior image quality on typical images. The luminance channel of the proposed method outperforms by 6.34-dB peak SNR the bilinear method, and the chrominance channels have a 7.69-dB peak signal-to-noise ratio improvement on average. Furthermore, the complexity of the proposed method is comparable to conventional bilinear interpolation. It requires only add and shift operations to implement.

In this paper, we propose a novel allpass (AP) fractional delay (FD) filter whose denominator polynomial is obtained by truncating the power series of a certain function. This function is derived from the frequency response of the denominator whose magnitude response is related to the desired. phase response through the Hilbert transform since the denominator of a stable AP filter is of minimum phase. The target function and corresponding power series are calculated. analytically and expressed in closed form. The closed-form expressions facilitate the analysis of stability. According to the properties for the coefficients of the denominator polynomial, we show that the proposed AP filter is stable for positive delay. Numerical examples indicate that the phase delays of the proposed filters are flat around ω = 0.

Since channel capacity varies depending on the network traffic and the capacity of each reception, fine granularity scalability (FGS) of video coding has emerged over the past years as an important area in multimedia streaming applications. We propose a FGS video codec and a two-layer SNR scalable video codec. Both of these are based on matching pursuits (MP). The bit plane atom coding is presented to achieve the SNR scalable matching pursuits. We also propose a differential quadtree-based algorithm to encode atom positions efficiently. The, performance of our methods are compared with those of H.263+ and DCT-based FGS coder.

In this paper, we propose a robust face detection method in color images, and it is suitable for various faces and under different illuminations. The pre-processing is to convert the 3-D RGB color histogram into 2-D R-Y/B-Y color histogram and to introduce the concept of flesh tone. The second procedure is the kernel processing, which is 2-D color histogram normalization, to eliminate the: affine effect of the color histograms due to the illuminations changing. We propose the new standard flesh region by using statistics in the normalized domain, then extract the candidates of the flesh regions. And the post-processing is to use connected operators, some criterions and thresholds to obtain accurate face regions. Experimental results show that the face detection is successful and satisfactory for the synthetic images and the real images.

For video scene analysis, the wipe transition is considered most complex and difficult to detect. In this paper, an effective wipe detection method is proposed using the macroblock (MB) information of the MPEG compressed video. By analyzing the prediction directions of B frames, which are revealed in the MB types, the scene change region of each frame can be found. Once the accumulation of the scene change regions covers most of the area of the frame, the sequence will be considered a motionless wipe transition sequence. Besides, uncommon intracoded MB of the B frame can also be applied as an indicator of the motion wipe transition. A very simple analysis based on small amount of MB type information is sufficient to achieve wipe detection directly on MPEG compressed video. Easy extraction of MB type information, low-complexity analysis algorithm and robustness to arbitrary shape and direction of wipe transitions are the great advantages of the proposed method.

The Fourier transform can be generalized into the fractional Fourier transform (FRFT), linear canonical transform (LCT), and simplified fractional Fourier transform (SFRFT). They extend the utilities of original Fourier transform, and can solve many problems that can not be solved well by original Fourier transform. We generalize the cosine transform. We derive the fractional cosine transform (FRCT), canonical cosine transform (CCT), and simplified fractional cosine transform (SFRCT). We show that they are very similar to the FRFT, LCT, and SFRFT, but they are much more efficient for dealing with the even, real even functions. For digital implementation, FRCT and CCT can save 1/2 of the real number multiplications, and SFRCT can save 3/4. We also discuss their applications, such as optical system analysis and space-variant pattern recognition.

It is popular to use the conventional correlation for pattern recognition. But when using the conventional correlation, the pattern should be the gray-level pattern. In this paper, we discuss how to use discrete quaternion correlation (DQCR) for the application of color pattern recognition. With the algorithm introduced here, we can detect the objects that have the same shape, color, and brightness as the reference pattern. Besides, we can also detect (a) the objects with the same shape, color, but different brightness, (b) the objects with the same shape, brightness, but different color, and (c) the objects just have the same shape as the reference. Our algorithm can classify the objects into 5 classes due to whether their shape, brightness, and color match those of the reference pattern. Besides, with our algorithm, the difference of the brightness and color can also be calculated at the same time.

This paper presents a general approach to find the shortest path for a general moving object with rotation and forward/backward movement among obstacles of arbitrary shapes. We call the object of finding a shortest path by the name of path planning. By utilizing the concept of the critical transition point and adaptive path planning, finding a shortest path problem of car-like vehicles becomes more practical. Moreover, additional efficiency in routing can be obtained since the critical transition point is used in the configuration space. Notice that the computational complexity is not increased. A car-like vehicle model with forward/backward driving and turning mechanism is used to validate the performance of the proposed algorithms. Simulation results show that not only are the proposed algorithms successful in various environments, but also these algorithms have good efficiency in computation. Moreover, routing gains with the help of morphological theory.

The affine Fourier transform (AFT) also called as the canonical transform. It generalizes the fractional Fourier transform (FRFT), Fresnel transform, scaling operation, etc., and is a very useful tool for signal processing. We derive the eigenfunctions of the AFT. The eigenfunctions seems hard to be derived, but since the AFT can be represented by the time-frequency matrix (TF matrix), we can use the matrix operations to derive its eigenfunctions. Then, because many optical systems can be represented as a special case of the AFT, the eigenfunctions of the AFT are just the light distributions that will cause the self-imaging phenomena for some optical systems. We use the eigenfunctions we derive to discuss the self-imaging phenomena.

In this paper, we propose a closed-form design of the generalized maximally flat low-pass FIR filters. By representing the transfer function as the Bernstein polynomial form, a simple generating function of the weighting coefficients is derived. We show that the linear phase maximally flat FIR filters and the nonlinear phase maximally flat half-band FIR filters are both special cases of the proposed filter. Closed-form expressions of both linear and nonlinear phase maximally flat FIR filters with prescribed degrees of flatness and delay can be easily obtained by the proposed method.

We propose an effective and efficient wipe detection method based on the macroblock information of the MPEG compressed video. Two types of wipe transitions are taken into consideration. By analyzing the prediction directions of B frames, which are revealed in the MB types, the scene change region of each frame can be found. Once the accumulation of the scene change regions covers most area of the frame, the sequence will be considered a wipe transition sequence. Besides, uncommon intra-coded MBs of the B frame can also be applied as an indicator of the wipe transition. A very simple analysis based on small amount of MB type information is sufficient to achieve wipe detection directly on MPEG compressed video.

We propose an effective color filter array interpolation method for digital still cameras using a simple image model that correlates the R, G, B channels. The main contribution of this paper is that we propose a low complexity interpolation method to improve the image quality. Simulation results verify that the proposed method obtain superior image quality. The G channel of the proposed method outperforms the bilinear method by 6.34 dB, and the R, B channels have a 7.69 dB improvement in average. Furthermore, the complexity of the proposed method is acceptable compared with the existing methods.

Many display devices now allow a number of colors, called color palette, to be displayed simultaneously. Besides, images and videos in most world wide web (WWW) databases are in compressed formats. Therefore, it becomes an important issue to retrieve a suitable color palette from compressed domain in order to have fast and faithful color reproduction for these devices. In this paper, the color palette design methods for compressed videos are presented. The proposed approaches use the reduced image rather than the whole image for the color palette design to avoid the heavy computation in video decompression. Experimental results show that output image quality of proposed methods is acceptable, to human eyes. In addition, empirical results show that the proposed shifting window scheme can reduce the main problem of displaying quantized image sequences and screen flicker.

DFT has good quality of performance and fast algorithms. But when we implement the DFT, we require the floating-point multiplication. In this paper, we introduce the integer Fourier transform (ITFT). ITFT is approximated to the DFT, but all the entries in the transform matrix are integer numbers. So it only requires fixed-point multiplication, and the implementation can be much simplified, especially for VLSI. This new transform will work similarly to the original DFT, for example, the transform results are similar and the shifting-invariant property is also preserved for ITFT. We also introduce the general method to derive the integer transform. By this approach, we can derive many types of integer transforms (such as integer cosine, sine, and Hartley transforms).

In this paper, we derive some properties of maximally flat R-regular Mth-band FIR filters. We show that the R-regularity implies maximally flat frequency response at /spl omega/=0. The R-regular constraints are a set of linear equations with complex coefficients. We can convert these complex-value equations to equivalent ones with only real coefficients. We also show that it is possible to completely determine the filter coefficients by R-regularity. Design examples are presented to illustrate the R-regularity properties and the effectiveness of the proposed approach.

In this paper, the design problems of the fractional Hilbert transformer (FHT) are investigated. First, the conventional Hilbert transformer is generalized to FHT and its corresponding analytic signal is also defined to construct a single side-band (SSB) signal for saving communication bandwidth. Then, several methods are presented to design FIR and IIR fractional Hilbert transformers including a Hilbert transformer based method and an allpass filter based method. Finally, several design examples are presented to demonstrate the effectiveness of the proposed methods.

In this letter, a closed-form expression for the impulse response of the generalized half-band (HB) maximally flat (MF) FIR filters is obtained by solving the linear equations of the MF conditions. Based on the resultant impulse responses, an efficient implementation structure is derived. The dynamic range of the multipliers of the new structure is shown to be greatly reduced in comparison to the one of the direct form impulse response.

In this paper, we propose a design of two-dimensional (2-D) linear-phase, diamond-shaped (DS) finite impulse response (FIR) filters by using Bernstein polynomials. Although the one-dimensional (1-D) FIR filter designed by the Bernstein polynomials has been well investigated, this approach has not been broadly applied to 2-D filter design yet. We present a novel method of designing the 2-D FIR DS filter. In order to be approximated by a 2-D Bernstein polynomial, the 2-D symmetrical frequency response is transformed into a new domain. The key observation is that the region of support of the transformed frequency response is not diamond-shaped. The boundary of the new region of support represents an ellipse, a circle, or a line, and is analytically derived. The resultant magnitude responses are flat in the passband and stopband.

Many display devices nowadays still allow a limited number of colors, called color palette, to be displayed simultaneously. Besides, images and videos in most World Wide Web databases are in compressed formats. Therefore, it becomes an important issue to retrieve a suitable color palette from compressed domain in order to have fast and faithful color reproduction for these devices. In this paper, the color palette design methods for compressed images and videos are presented. The proposed approaches use the reduced, rather than the whole, image for the color palette design to avoid the heavy computation in image or video decompression. Also, for compressed videos, a shifting-window scheme is proposed to smooth out color variations in the change of color palette. In these methods, we extend the dependent scalar quantization algorithm of a single image to accomplish the color palette design. Experimental results show that the output image quality of the proposed methods is acceptable to human eyes. In addition, empirical results show that the proposed shifting-window scheme can reduce the main problem of displaying quantized image sequences, screen flicker.

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces the 1-D Fourier transform by the l-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) of Sahin, Ozaktas and Mendlovic (see Appl. Opt., vol.37, no.11, p.2130-41, 1998). It also has been generalized into the 2-D unseparable fractional Fourier transform with 4 parameters of Sahin et al. (see Appl. Opt., vol.37, no.23, p.5444-53, 1998). In this paper, we introduce the 2-D affine generalized fractional Fourier transform (AGFFT). These 2-D transforms has been further generalized. We show it can deal with many problems that can not be dealt with by these 2-D transforms and extend their utility.

Segmentation is an important step for image analysis, but a good segment algorithm which can handle color image with texture area and has less computation time is rare. We propose to use the local window image histogram, which is easy to compute and could quickly collect the information of neighbors, together with the Self-Organization of Kohonen Feature Map (SOFM) neural network, which can efficiently cluster data and has parallel hardware structure, as a segmentation kernel. Under the Euclidean distance function with input data normalization and the simplified Mahalanobis distance function, this algorithm will have very good segmentation results for natural images either full with texture or mixed with smooth scenes.

Color-based indexing is an important tool in image database retrieval. Compared with other features of the image, color features are less sensitive to noise and background complication. Based on the human visual system's perception of color information, this paper presents a dependent scalar quantization approach to extract the characteristic colors of an image as color features. The characteristic colors are suitably arranged in order to obtain a sequence of feature vectors. Using this sequence of feature vectors, a dynamic matching method is then employed to match the query image with database images for a nonstationary identification environment. The empirical results show that the characteristic colors are reliable color features for image database retrieval. In addition, the proposed matching method has acceptable accuracy of image retrieval compared with existing methods.

This paper presents a new moment-preserving thresholding technique, called the binary quaternion-moment-preserving (BQMP) thresholding, for color image data. Based on representing color data by the quaternions, the statistical parameters of color data can be expressed through the definition of quaternion moments. Analytical formulas of the BQMP thresholding can thus be determined by using the algebra of the quaternions. The computation time for the BQMP thresholding is of order of the data size. By using the BQMP thresholding, quaternion-moment-based operators are designed for the application of color image processing, such as color image compression, multiclass clustering of color data, and subpixel color edge detection. The experimental results show that the proposed operator for color image compression can have output picture quality acceptable to human eyes. In addition, the proposed edge operator can detect the color edge at the subpixel level. Therefore, the proposed BQMP thresholding can be used as a tool for color image processing.

The covariance matrix of a pattern is composed by its second order central moments. For a rotationally symmetric shape, its covariance matrix is a scalar identity matrix. In this work, we apply this property to restore the skewed shape of rotational symmetry. The relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived. By computing the covariance matrix of the skewed shape and letting the covariance matrix of the original shape be a scalar identity matrix, the skew transformation matrix can be solved. Then, the rotationally symmetric shape can be recovered by multiplying the inverse transformation matrix with the skewed shape. The method does not rely on continuous contours and is robust to noise, because only the second-order moments of the input shape are required. Experimental results are also presented.

Efficient indexing methods are required to handle the rapidly increasing amount of visual information within video databases. Video analysis that partitions the video into clips or extracts interesting frames is an important preprocessing step for video indexing. We develop a novel method for video analysis using the macroblock (MB) type information of MPEG compressed video bitstreams. This method exploits the comparison operations performed in the motion estimation procedure, which results in specific characteristics of the MB type information when scene changes occur or some special effects are applied. Only a simple analysis on MB types of frames is needed to achieve very fast scene change, gradual transition, flashlight, and caption detection. The advantages of this novel approach are its direct extraction from the MPEG bitstreams after VLC decoding, very low complexity analysis, frame-based detection accuracy and high sensitivity.

This paper is concerned with the definition of the continuous fractional Hartley transform. First, a general theory of the linear fractional transform is presented to provide a systematic procedure to define the fractional version of any well-known linear transforms. Then, the results of general theory are used to derive the definitions of the fractional Fourier transform (FRFT) and fractional Hartley transform (FRHT) which satisfy the boundary conditions and additive property simultaneously. Next, an important relationship between FRFT and FRHT is described. Finally, a numerical example is illustrated to demonstrate the transform results of the delta function of FRHT.

A strategy for efficiently coding stereo video sequences is investigated. To fully utilize the suppression and the contrast sensitivity property of the human visual system, a novel coding scheme with two special mechanisms, the spatiotemporal HVS model and the binary correlation disparity estimator, is proposed to efficiently reduce the video signal redundancy and the computational complexity, while maintaining a high subjective image quality. Compared with existing stereo video coding systems, the proposed coding scheme supports a lower transmission bit rate and has less computational complexity. The simulation results also show that the subjective image quality of the reconstructed full color stereo sequences at 0.25-0.4 bits per pixel (bpp) is satisfactory.

Performance of fractionally spaced equalizers using polyperiodic linear filtering is depicted. The fractionally sampled version of an arbitrary stable channel's outputs with stationary random inputs exhibit cyclostationarity with cycle frequencies being integer multiples of the reciprocal of the oversampling factor. By optimally polyperiodic linear filtering the oversampled outputs, we can fully utilize the cyclostationary property. With some traditional Bussgang techniques, such as stop-and-go decision-directed method, to adaptively update the filter coefficients, the convergence rate of the fractionally spaced equalizers proposed is improved, while the complexity retains in the same order as original Bussgang ones. Some computer simulation results are shown to demonstrate the improvement we can achieve.

A video coding method called model-based image coding has attracted much attention as a potential candidate for low bit-rate visual communication services. This technique reconstructs the facial image with a preknown 3D human face model and its received model motion parameters. The parameters of the head motion are mainly divided into two parts: global motion parameters describe the rigid movement of the head, such as rotation and translation, and local motion parameters which deal with the nonrigid movements of facial expressions, such as the opening and closing of the mouth and eyes. In this paper, we propose a new approach which can estimate the head global motion more robustly and accurately. Comparing with the existing techniques to match only a few key points, here we extract 3-D contour feature points and use chamfer distance matching to estimate head global motion. This can improve and enhance the contour tracking performance greatly. We also develop another technique called facial normalization transform. It maps the facial region of the current input frame back to the normalized pose of the initial frame. Using this transform, we can analyze facial expressions at the same orientation and fixed region. This simplifies the analysis work a lot. Then, we do our encoding by the clip-and-paste method along with adaptive codebook technique. In the following the coder and decoder system are briefly described.

Several methods have been proposed to do color quantization for limited color displays. Self-organization of Kohonen feature maps (SOFM) is a very useful tool for data clustering. By extracting a special butterfly-jumping sequence from an image, a neural network was fed in that sequence of image data for SOFM training, and a fairly good color table was present to represent that image. The peak signal-to-noise ratio of the decoded image is high (about 35 dB in average for a 256 color image), and the perceptual quality is good as well, even with a small set of color tables (for example, 32 or 64 colors). Furthermore, the training process is fast. For encoding, we also propose an efficient algorithm based on the Kohonen map ordering property. By considering that the neighboring image pixels are closely related and by setting some acceptable thresholds, we can quickly get an encoded image. For further compression on the color indexed image with the limited color palette, we cut the indexed images into 4/spl times/4 blocks and send the block vectors into another SOFM neural network for training. Under the two-dimensional (2-D) mesh neural structure, SOFM vector quantization on an indexed image could largely reduce the color shift artifacts and avoid the requantization problem. About 0.5 b per pixel of coded image can be easily obtained with a fairly good perceptual quality. More importantly, the decoded color indexed images can be readily displayed. This will reduce the decoder complexity greatly.

We propose an algorithm to solve the path planning problem in an automated vehicle guidance system. Many methods have been proposed to solve such a problem, but, none of them takes as many practical factors into consideration. Although the literature dealt with one or more of the above factors separately, none had included them in a single research. We have included the following factors into our model: size and orientation, intended directions, driving costs, and obstacles. A powerful but simple algorithm based on the constrained distance transformation is shown to: (1) determine the feasibility given the start and finish positions; (2) find the optimal collision-free driving path which minimizes the total driving cost subject to the constraints; (3) provide a smooth path.

This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions which are eigenfunctions of the continuous Fourier transform and by performing a novel error removal procedure. Then, the result of the eigendecomposition of the DFT matrix is used to define a new DFRFT. Finally, a numerical example is illustrated to demonstrate the proposed DFRFT is a better approximation to the continuous fractional Fourier transform than the conventional defined DFRFT.

Block truncation coding (BTC) is an efficient tool for image compression. To compress color-pixel blocks, a novel color BTC algorithm, called quaternion-moment block truncation coding (QMBTC), is presented. Analytical formulas for QMBTC, whose computation time is on the order of pixel block size, are derived by using quaternion arithmetic and the moment-preserving principle. The proposed color BTC algorithm can adaptively truncate a pixel block into one or two output classes according to the distribution of the color values inside the blocks. The experimental results show that the compression ratio is increased as compared with existing color BTC algorithms, and the picture quality of the reconstructed images is satisfactory. In addition, a post-BTC data compression scheme is proposed to further compress the subimage constructed by reproduction colors of truncated pixel blocks. Using a lookup table to display decoded data, this postprocessing scheme can output images acceptable to human eyes.

The goal of three-dimensional (3-D) motion segmentation is to identify the image areas projected by different moving objects in 3-D space. However, many prevailing methods merely detected the discontinuity of optical flow field and usually considered these boundaries as that produced by different 3-D motions. In fact, the flow discontinuity can be generated either by two different 3-D motions or by the structural discontinuity on the same moving object. The wrong identification causes several problems in 3-D motion estimation. A simple method called the extrapolation and subtraction (ES) technique is proposed to solve these problems. The input image flow field is first partitioned into several functionally analytic regions. Each analytic region is assumed to be projected by a roughly planar patch moving in 3-D space. Based on the parameterization of these analytic flow fields, the ES technique provides a very simple and fast method to test the 3-D motion compatibility between two interested analytic flow fields.

The covariance matrix of a rotationally symmetric shape is a scalar identity matrix. We apply this property of covariance matrix to deskew the skewed shape of rotational symmetry. The parameters of the deskew transformation matrix are solved by letting the covariance matrix of the transformed shape be equal to a scalar identity matrix. Then, the rotationally symmetric shape can be recovered by the deskew transformation matrix. The method does not rely on continuous contours, since only second-order moments of the input shape are required to be computed. Experimental results are also presented.

The Hough transform technique has been applied to detect rotational symmetry by Yip et al. (1994). He proposed an O(N/sup 3/) algorithm, where N is the number of edge points in the input image, to extract global or local features of rotational symmetry in the presence of noise and occlusion. In this paper, we follow the Yip et al. concept and design a simple and efficient algorithm, which can detect the rotational symmetry in O(N/sup 2/) time. Some simulation results of the new proposed algorithm are also given.

Iterated function systems (IFSs) have received great attention in encoding and decoding fractal images. Barnsley (1988) has shown that IFSs for image compression can achieve a very high compression ratio for a single image. However, the major drawback of such a technique is the large computation load required to both encode and decode a fractal image. We provide a novel algorithm to decode IFS codes. The main features of this algorithm are that it is very suitable for parallel implementation and has no transient behavior. Also, from the decoding process of this method we can understand the encoding procedure explicitly. One example is illustrated to demonstrate the quality of its performance.

The relationship between the finite discrete Zak transform and the finite Gabor expansion are discussed in this paper. We present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other upon the frequency-split Zak transform. These two methods are time and frequency dual pairs. Furthermore, we extend the relationship between the finite discrete Zak transform and the Gabor expansion to the 2-D case and compute 2-D Gabor expansion coefficients through the 2-D discrete Zak transform and 4-D DFT. Four methods can be applied in the 2-D case. They are time-time-split, time-frequency-split, frequency-time-split and frequency-frequency-split.

Many image display devices can allow only a limited number of colors, called color palette, to be simultaneously displayed. In order to have a faithful color reproduction of an image, the associated color palette must be suitably designed. This paper presents a dependent scalar quantization algorithm to design the color palette effectively. The dependent scalar quantization algorithm consists of two procedures, bit allocation and recursive binary moment preserving thresholding. The experimental results show that the dependent scalar quantization can reduce the computation complexity and its output images quality is acceptable to the human eyes. A rule of the quantization order is also deduced under the MSE criterion to obtain a dependent scalar quantizer which has as good a performance as compared with some other algorithms. In addition, an adaptive neighborhood-clustering algorithm, which searches the neighboring color indices of input pixels iteratively, is proposed to further improve the performance of the dependent scalar quantization algorithm. Finally, we introduce a color mapping method to reduce the contouring effect when the color palette size generated by the dependent scalar quantizer is small.>

In this correspondence, we consider wavelet transform and scale space filtering as special cases of general scale shift mapping (SSM). Then, the SSM is used as a tool for characterizing the geometrical complexity of uniform fractals. This tool can reveal the construction rule of fractals and estimate fractal dimension. Finally, we use the results obtained from scale shift mapping to estimate iterated function system (IFS) codes of a class of fractal images. Some examples have been illustrated to demonstrate its good performance.

A technique for suppressing the transient states of IIR notch filters is presented. This technique mainly uses the vector projection to find the best initialization of a notch filter. When a notch filter is used to cancel 60 Hz interference in the recording of electrocardiograms (ECG), the performance of the notch filter with transient suppression is better than that of the notch filter with arbitrary initialization. The improvements realized by this technique is at the cost of little additional computational load at the beginning of filtering.>

A new two dimensional (2D) adaptive filter structure is developed. It is based on modeling the impulse response of the 2D IIR systems as a finite linear combination of a set of 2D Laguerre orthonormal functions. When it is required to identify a system with a long impulse response, computer simulation shows that the 2D Laguerre filter has a better performance than the conventional 2D FIR filter at the same computation cost.>

We propose a method to detect circular arcs, including the determinations of their centers, radii, lengths, and midpoints. The center, radius of a circular arc can easily be determined using circular Hough transform. But, the determinations of the arc midpoint and length are more complicated. Theoretical analysis of the centroid of the near-peak Hough transform data is presented. Then, the arc midpoint and length can be extracted from it.>

An adaptive FIR filter based on the least mean p-power error (MPE) criterion is investigated. First, some useful properties of MPE function are studied. Three main results are as follows: 1) MPE function is a convex function of filter coefficients; so it has no local minima. 2) When input process and desired process are both Gaussian processes, then MPE function has the same optimum solution as the conventional Wiener solution for any p. 3) When input process and desired process are non-Gaussian processes, then MPE function may have better optimum solution than Wiener solution. Next, a least mean p-power (LMP) error adaptive algorithm is derived and some application examples are presented. Consequently, when the signal is corrupted by an impulsive noise, the adaptive algorithm with p=1 is preferred. Furthermore, when the signal is corrupted by noise or interference, the adaptive algorithm with proper choice of p may be preferred.>

By minimizing a quadratic measure of the error in the passband and stopband, a 2-D diamond-shaped finite impulse response, (FIR) eigenfilter is designed for sampling-structure conversion. Time- and frequency-domain constraints, are easily incorporated into this method, such that the design difficulty inherent to sample-conversion filters can be effectively solved. A design example and simulation with test pictures are presented to demonstrate the effectiveness of the approach.>

It is shown that there exists a close relationship among digital one/half band filters, low/high order differentiators, and discrete/differentiating Hilbert transformers. An attempt is made to present a complete picture of their interrelationships and conversions between one another. A table and some block diagrams have been developed for their impulse response connections, and a design example is also given for illustration.>

A fast algorithm for computing the pseudo-Wigner distribution using the fast Hartley transform (FHT) is presented. Unlike the conventional fast Fourier transform (FFT) approach, this algorithm performs entirely in the real domain. Many efficient FHT algorithms can be applied, and the computation complexity is reduced from three complex FFTs to three real FHTs.>

An efficient subband image decomposition method by mathematical morphology is described in this paper, it decomposes the input signal spectrum into 4 subband images by using two separable structure elements, then each band image, can be decimated and coded effectively for data transmission. This subband pyramid scheme preserves the number of pixels as in the original image, also the data structure itself is very compact, the advantages of morphology over linear filtering approach are its direct geometric interpretations, simplicity and efficiency in implementation, some image examples are given to show the effectiveness of this approach.

This paper describes a complex log mapping approach to 2D color object recognition. First a 3D vector color image is first transformed into a 2D vector image by projection into a color plane, then complex log mapping transform is applied on this 2D vector color image for invariant pattern recognition; By extensive computer simulations, this method can effectively recognize a scale and rotation changed color object among the similar shape objects but with different colors, and also among the different shape objects as well very successfully.

The morphological pyramid is a new computationally efficient algorithm for generating multidimensional bandpass representation of an image. This image pyramid offers a flexible convenient multiresolution format that mirrors the multiple scales of processing in the human visual system. Here the morphological pyramid is used for image mosaic and smear removal by multiresolution interpolation, some image examples are illustrated to show the effectiveness of this approach.

This paper deals with the design of 2D multiplierless FIR digital filters, first a special class of multiplierless 1D FIR filters are designed with coefficients which are a sum or difference of power-of-two, and then map it into 2D multiplierless FIR filters by McClellan transform; This technique has the advantage that it is very fast, because only a 1-D filter must be designed, also the hardware implementation for these 2D FIR filters is very attractive and efficient.

Split vector radix is used to develop a 2D fast Fourier transform algorithm, it is performed "in-place", and requires no matrix transpose operation; This method greatly improves the conventional vector radix 2D FFT, an overall saving of about 30% complex multiplications for a typical 1024 × 1024 array could be obtained.

In this paper, an efficient method to do the digital convolution of rational numbers is proposed. The inefficient P-adic arithmetic is replaced by the integer arithmetic, in this new approach. Furthermore, since rational number are exactly representable, error-free results of the convolution of two rational sequences can be obtained by this method very efficiently.

The 2D forward and inverse discrete cosine transforms (DCT) are mapped by polynomial transforms into several one-dimensional DFTs; This algorithm is more attractive for computing the "inverse" 2D DCT, it nicely eliminates N2premultiplications for the forward algorithm, and requires only N reduced real DFTs of size 2N; This inverse 2D DCT algorithm is 3 times faster than the forward one, more importantly it requires much less computation complexity than the most efficient recent algorithms.

The inherent nonseparable difficulty in 2D hexagonal sampled data can be overcome by choosing suitable periodicity and sampling basis, this will turn the original hexagonal data into very simple separable parallelograms, and then the rectangular polynomial transforms can be used to efficiently calculate 2D hexagonal convolutions; This algorithm is much faster than the hexagonal discrete Fourier transform method.

McClellan's transformations for 2D FIR filter design are sliced into several 1D frequency transforms for linear phase variable filters. Each transform maps 1D prototype FIR filter into several one dimensional variable cut-off digital filters in the 2D frequency plane; This approach is equivalent to the conventional McClellan's transformation, however the complicated 2D transformation steps are reduced into the simple 1D forms, the algorithm is much easier to implement and has additional advantage to design the nonsquare 2D FIR filters.

System performance is substantially enhanced by using good attenuators in the system and employing a pulsing mode of operation. Spurious image elements, due to multiple reflections of the ultrasound in the acoustic cell and due to echoes from elements in the system which are not part of the object plane being imaged, can be eliminated in this fashion. In addition, depth discrimination can be substantially improved, in agreement with theory.