Point-interactive image colorization is intended to colorize a grayscale image by allowing the user to specify colors at specific locations. The colors provided by the user (user hints) are propagated appropriately throughout the image to obtain a reasonably colorized image with minimal user effort. However, existing approaches result in excessive color propagation and color bleeding beyond the boundaries of the region. To address this problem, we propose iReWindColor. iReWindColor achieves fine colorization by using smaller patches for Vision Transformer-based processing. Due to the increase in computational cost caused by reducing the patch size, the processing for the entire image is replaced by Window Encoder, which is the window-based processing. This allows fine colorization with small patches without increasing the computational cost. In addition, we propose Residual Embaedding to reduce colorization divergence between windows. Residual Embedding makes the network consider the entire image. Furthermore, for better utilizing user hints, we propose Encode Block that consists of both Self-Attention and CNNs. Adopting it helps to capture the interrelationships between image patches. Quantitative and qualitative results show that our approach outperforms existing methods for point-interactive image colorization and produces color images that accurately reflect user intent with less computation cost.

2D pose estimation is a fundamental task predicting geometric construction of targets like a human and an animal from input images. Notably, we focus on characters that are drawn on canvas, such as illustrations and paintings. Poses of the characters can be used for many applications, such as a retrieval system and detecting plagiarism. However, it is difficult to identify the poses because of domain characteristics. In this paper, we tackle that domain issue by developing Series and Parallel Dilated Convolution (SPDC), which is based on an inverted residual bottleneck and has cascade connections and parallel connections simultaneously. In addition, we propose Style Channel Attention (SCA), which reflects style information of an input image in estimation. These modules can deal with different painting styles and parts of characters. Compared with existing methods, our method improves average precision by 2.89 % and average recall by 2.58 % in evaluating the results with an illustration dataset.

We propose PoE-Diffusion, a framework that incorporates the Product of Experts (PoE) into diffusion models. PoE-Diffusion enables sampling from a weighted product of probability distributions across multiple diffusion models without additional training. As an application of PoE-Diffusion, we introduce Pseudo-finetuning and evaluate it through experiments. We demonstrate that Pseudo-finetuning generates high-quality images with short training time, supported by both qualitative and quantitative results. PoE-Diffusion can be applied to any existing diffusion models as it only affects the inference process. This approach has the potential to be applied to a wide range of tasks that using diffusion model.

Shadow removal is an essential task in image processing and high-level vision applications. While recent methods with window-based attention have shown promising results, their limited ability to exchange information across local windows often leads to suboptimal performance in complex shadow scenarios. In this paper, we propose WPRFormer, a novel shadow removal framework that incorporates Window-Aware Pixel Rearrangement (WPR) into the attention module to facilitate more effective spatial interactions beyond individual windows. Since WPR rearranges pixels based on their original spatial layout, it largely preserves relative positional information within each window, allowing for the use of relative position bias without significant distortion. Our framework applies WPR Blocks at multiple resolution levels, enhancing feature representation while maintaining computational efficiency. Experimental results demonstrate that our method consistently outperforms existing approaches in both shadow and non-shadow regions, with particularly notable improvements in challenging shadow region, all while maintaining a comparable model complexity to strong baselines.

Face photo-sketch synthesis tasks have been developed with Generative Adversarial Networks (GANs) based on Convolutional Neural Network (CNN) and Vision Transformer (ViT). CNN is good at capturing local features, but its locality results in blurred images and contours. ViT is good at capturing global information, but is not as good as CNN in capturing local features, and while it can prevent blurring of contours and other lines, it does not reflect fine texture. Therefore, we propose a Face Drawing GAN, which generates high-quality face sketches by capturing both local and global features. Face Drawing GAN is a CNN-based model and it incorporates Channel Attention, which functionally adjusts the weights of channels, and Matrix Product Attention (MP Attention), which weights pixels based on the similarity between the vertical and horizontal sides of images obtained by matrix product. Through the experiments, we confirmed that our proposed MP Attention assists in capturing global features and Face Drawing GAN is capable of generating face sketches that outperform conventional methods.

Video super-resolution aims at generating high-resolution video frames using multiple adjacent low-resolution frames. An important aspect of video super-resolution is the alignment of neighboring frames to the reference frame. Previous methods directly align the frames either using optical flow or deformable convolution. However, directly estimating the motion from low-resolution inputs is hard since they often contain blur and noise that hinder the image quality. To address this problem, we propose to conduct feature alignment across multiple stages to more accurately align the frames. Furthermore, to fuse the aligned features, we introduce a novel Attentional Feature Fusion Block that applies a spatial attention mechanism to avoid areas with occlusion or misalignment. Experimental results show that the proposed method achieves competitive performance to other state-of-the-art super-resolution methods while reducing the network parameters.

Underwater images suffer from low contrast, color distortion and visibility degradation due to the light scattering and attenuation. Over the past few years, the importance of underwater image enhancement has increased because of ocean engineering and underwater robotics. Existing underwater image enhancement methods are based on various assumptions. However, it is almost impossible to define appropriate assumptions for underwater images due to the diversity of underwater images. Therefore, they are only effective for specific types of underwater images. Recently, underwater image enhancement algorisms using CNNs and GANS have been proposed, but they are not as advanced as other image processing methods due to the lack of suitable training data sets and the complexity of the issues. To solve the problems, we propose a novel underwater image enhancement method which combines the residual feature attention block and novel combination of multi-scale and multi-patch structure. Multi-patch network extracts local features to adjust to various underwater images which are often Non-homogeneous. In addition, our network includes multi-scale network which is often effective for image restoration. Experimental results show that our proposed method outperforms the conventional method for various types of images.

In recent years, accurate Gaussian noise removal has attracted considerable attention for mobile applications, as in smart phones. Accurate conventional denoising methods have the potential ability to improve denoising performance with no additional time. Therefore, we propose a rapid post-processing method for Gaussian noise removal in this paper. Block matching and 3D filtering and weighted nuclear norm minimization are utilized to suppress noise. Although these nonlocal image denoising methods have quantitatively high performance, some fine image details are lacking due to the loss of high frequency information. To tackle this problem, an improvement to the pioneering RAISR approach (rapid and accurate image super-resolution), is applied to rapidly post-process the denoised image. It gives performance comparable to state-of-the-art super-resolution techniques at low computational cost, preserving important image structures well. Our modification is to reduce the hash classes for the patches extracted from the denoised image and the pixels from the ground truth to 18 filters by two improvements: geometric conversion and reduction of the strength classes. In addition, following RAISR, the census transform is exploited by blending the image processed by noise removal methods with the filtered one to achieve artifact-free results. Experimental results demonstrate that higher quality and more pleasant visual results can be achieved than by other methods, efficiently and with low memory requirements.

Video frame interpolation aims to generate intermediate frames between the original frames. This produces videos with a higher frame r ate and creates smoother motion. Many video frame interpolation methods first estimate the motion vector between the input frames and then synthesizes the intermediate frame based on the motion. However, these methods rely on the accuracy of the motion estimation step and fail to accurately generate the interpolated frame when the estimated motion vectors are inaccurate. Therefore, to avoid the uncertainties caused by motion estimation, this paper proposes a method that directly generates the intermediate frame. Since two consecutive frames are relatively similar, our method takes the average of these two frames and utilizes residual learning to learn the difference between the average of these frames and the ground truth middle frame. In addition, our method uses Convolutional LSTMs and four input frames to better incorporate spatiotemporal information. This neural network can be easily trained end to end without difficult to obtain data such as optical flow. Our experimental results show that the proposed method can perform favorably against other state-of-the-art frame interpolation methods.

In this paper, we propose high quality image deblurring by using discrete cosine transform (DCT) with less computational complexity. Recently, Convolutional Neural Network (CNN) and Generative Adversarial Network (GAN) based algorithms have been proposed for image deblurring. Moreover, multi-scale architecture of CNN restores blurred image cleary and suppresses more ringing artifacts or block noise, but it takes much time to process. To solve these problems, we propose a method that preserves texture and suppresses ringing artifacts in the restored image without multi-scale architecture using DCT based loss named “DeblurDCTGAN.”. It compares frequency domain of the images made from deblurred image and ground truth image by using DCT. Hereby, DeblurDCTGAN can reduce block noise or ringing artifacts while maintaining deblurring performance. Our experimental results show that DeblurDCTGAN gets the highest performances on both PSNR and SSIM comparing with other conventional methods in GoPro, DVD, NFS and HIDE test Dataset. Also, the running time per pair of DeblurDCTGAN is faster than others.

The removal of mixed noise is a stiff problem since the distribution of the noise cannot be predicted accurately. The most common mixed noise is the combination of Additive White Gaussian Noise (AWGN) and Impulse Noise (IN). Many methods first attempt to remove IN but it might collapse the texture of the image. In this paper, we propose a new learning-based method using convolutional neural network (CNN) for removing mixed gaussian-impulse noise. Since our denoising network can remove various level of mixed noise, neither the preprocessing for removing IN nor noise-level estimation is necessary.

Edge-preserving smoothing filter smoothes the textures while it preserves the information of sharp edges. In image processing, this filter is used as a fundamental process of many applications. In this paper, we propose a new approach for edge-preserving smoothing filter. Our method uses 2D filter to smooth images and we apply indicator function to restrict the range of filtered pixels for edge-preserving. To define the indicator function, we recalculate the distance between each pixel by using edge information. The nearby pixels in the new domain are used for smoothing. Since our method constrains the pixels used for filtering, its implementation is quite fast. We demonstrate the usefulness of our new edge-preserving smoothing method for some applications.

Rotation and scale estimation of images are fundamental tasks in image registration. The conventional estimation method uses log-polar transform and 1D shift estimation to estimate rotation and scale regardless of the shift of images. However, this transform requires interpolation of the frequency components, which causes estimation error. We propose a rotation and scale estimation algorithm based on Radon transform and sub-pixel shift estimation. Radon transform can estimate the rotation independent of the shift and can reduce the influence of interpolation error because it is performed on the spatial image rather than the frequency. In addition, sub-pixel shift estimation using linear approximation of the phase component improves the precision of 1D shift estimation and achieves accurate rotation estimation. The proposed method was evaluated on test images, and the results demonstrate that the proposed method accurately estimates rotation compared to log-polar-based and other conventional methods.

Many conventional demosaicking methods are based on hand-crafted filters. However, the filters yield false colors in salient regions like edges and textures. For acquisition of high quality images, we focus on neural networks. Neural networks lead to high accuracy in many fields. However, there are few methods in demosaicking field. For adaptation to demosaicking, we consider not only network's architecture but also the input. In this research, we utilize a Bayer image as input of our networks. However, different filter is needed in estimation at different color pixels, for example, missing red value at green pixel and that at blue pixel. Therefore, we prepare four networks with downsampling operators classified by color patterns in Bayer images. This downsampling operator not only identifies the color pattern but also reduces the calculation cost in each network due to reduction of the size of feature maps. Besides, preparation of multi-networks instead of a deep single-network is suitable for today's parallel computing. Moreover, we utilize not missing color images but chrominance images as output. Compared to results with missing color images as output, the results with chrominance images obtains higher accuracy. Experimental results show our CNN-based approach produces high quality restored images.

Underwater image enhancement is important for images captured in underwater because underwater images often suffer from color cast, low contrast and degraded visibility due to the absorption and scattering of light in water. In this paper, we propose a novel algorithm for underwater image restoration based on a generalization of the dark channel prior (GDCP). Though there are various types of underwater images, we especially focus on underwater images with depth because these images are not enhanced well by current algorithms. The proposed algorithm is composed of the iteration of GDCP and image fusion. Additionally, we introduce the new ambient light estimation to adapt to more types of images. Experimental results show that proposed algorithm is effective for various types of underwater images, especially for the images with depth.

Most outdoor vision systems can be influenced by rainy weather conditions. In this paper, we address a rain removal problem from a single image. Some existing de-raining methods suffer from hue change due to neglect of the information in low frequency layer. Others fail in assuming enough rainy image models. To solve them, we propose a residual deep network architecture called ResDerainNet. Based on the deep convolutional neural network (CNN), we learn the mapping relationship between rainy and residual images from data. Furthermore, for training, we synthesize rainy images considering various rain models. Specifically, we mainly focus on the composite models as well as orientations and scales of rain streaks. The experiments demonstrate that our proposed model is applicable to a variety of images. Compared with state-of-the-art methods, our proposed method achieves better results on both synthetic and real-world images.

This paper improves a colorization-based image coding using image segmentation and adaptive colorspaces. Recently, various approaches for color image coding based on colorization have been presented. These methods utilize a YCbCr colorspace and transfer the luminance component by a conventional compression method. Then, the chrominance components are approximated from the luminance component using a colorization method. Our method segments a luminance component into small segments called superpixels, and reconstructs the chrominance of each superpixel as a linear combination of its luminance. For chrominance components, we introduce an adaptive color space transform optimized for liner combination. This is because YCbCr colorspace cannot always become a good approximation of the chrominance. In addition, we introduce an automatic selection for the number of superpixel segments from a given quality factor. The simulation with standard images shows that our method performs better result than conventional coding schemes.

Image deconvolution is the task to recover the image information that was lost by taking photos with blur motion. Especially blind image deconvolution requires no prior informations other than the blurred image. This problem is seriously ill-posed and an additional operation is required such as extracting image features. In this paper, we present a blind image deconvolution framework using a specified highpass filter (HPF) for feature extraction to estimate a blur kernel. This problem can consider the kernel estimation in the region where salient edges are not present and improve the quality of the estimated kernel. Our approach also accelerates the deconvolution process by utilizing a conjugate gradient method in a frequency domain. This process eliminates costly convolution operations from the iterative updating and reduces the calculation time. Evaluation for 20 test images shows our framework not only performs faster than conventional frameworks but also improves the quality of recovered images.

Image upsampling from one input image gathers considerable attention in the field of computer vision. The problem is ill-posed because the number of known low-resolution (LR) pixels is less than that of unknown high-resolution (HR) pixels. Therefore, quality of an upsampled image depends on prior assumptions. Image interpolation methods are one of the image upsampling technologies and are faster than other image upsampling technologies such as Super-Resolution. However, these methods tend to cause jaggies and blurs in edge and texture regions. We use the idea of Multi-surface Fitting (MF) to solve these problems. MF uses plural local functions to estimate an HR pixel and it reduces blurs. Moreover, we utilize filtering instead of calculation of each local function in order to reduce a computational cost. And we introduce new weights to estimate edge directions. By these ideas, our method has both high quality and a low computational cost.

This paper aims to introduce an overcomplete transform based on fractional cycle spinning (FCS). Conventionally, the CS approach of wavelet transforms has been proposed, in order to achieve translation invariance with redundancy, unlike the classical critically sampled wavelet transform. This advantage contributes to efficient image processing, such as image denoising. The proposed FCS generalizes CS and show that richer overcompleteness can be provided by fractional shifts of input signals. For realizing fractional delay, we present the approach based on modulated lapped transforms (MLTs). It is shown that their filter kernels can express arbitrary fractional delay by carefully selecting their window function. In addition, this paper extend the conventional MLT to the dual-tree MLT to improve its poor directional selectivity. Then, an efficient lattice structure for the FCS is described for lower computational complexity. Finally experimental results show FCS can be applied better than the conventional CS in image denoising.

We present a realization of reversible lapped transforms (RevLTs) with simplified implementations, which are constructed by DCT and DST matrices, adders, and bit-shifters, for lossy-to-lossless image coding in this paper. Each DCT or DST matrix is directly used to each lifting coefficient block and it is called DCT-lifting structure. The structure is obtained by considering parallel processing of two `same' type LTs and using DCT-lifting factorizations as our previous work. Furthermore, the Hadamard transform and scaling parts in the RevLTs are effectively implemented by extending 2D non-separable lifting structures derived from lifting-based lapped transform (L-LT) used for JPEG XR, the newest image coding standard. As a result, the proposed RevLTs achieve not only simplified implementations with any block size, but also comparable lossy-to-lossless image coding performance to the conventional RevLTs.

This paper proposes NMF-based (non-negative matrix factorization) multiple pitch estimation algorithm. The approach of NMF-based multiple pitch estimation is to decompose input magnitude spectrogram into sum of basis spectra representing individual pitches. In decomposing music signals, the amplitude of basis spectra should have sparseness, and the shape of amplitude should be continuous between neighbor temporal frames. We introduce the constraint using matrix norm to enforce these characteristic at once and propose new NMF algorithm for spectral decomposition with this constraint. The evaluation of solo piano music shows this algorithm can implement more robust pitch estimation in the place which input spectrum has certain different shape from basis spectra or the shape of input spectrum has temporal change.

We present an effective image boundary processing for M-channel (M ∈ IN, M ≥ 2) lifting-based linear-phase filter banks that are applied to unified lossy and lossless image compression (coding), i.e., lossy-to-lossless image coding. The reversible symmetric extension we propose is achieved by manipulating building blocks on the image boundary and reawakening the symmetry of each building block that has been lost due to rounding error on each lifting step. In addition, complexity is reduced by extending nonexpansive convolution, called reversible symmetric nonexpansive convolution, because the number of input signals does not even temporarily increase. Our method not only achieves reversible boundary processing, but also is comparable with irreversible symmetric extension in lossy image coding and outperformed periodic extension in lossy-to-lossless image coding.

The multiplierless fast Fourier transform (FFT) with dyadic-valued (rational) coefficients is important for many signal processing tools. The proposed lifting based FFT (L-FFT) based on fast Hartley transform (FHT) has a simpler structure than existing ones because fewer lifting steps need to be approximated. In addition, it has a structure of real-valued calculation followed by complex-valued parts, thereby it requires fewer memories for the internal implementation than the conventional FFTs.

Complex-valued conjugate symmetric Hadamard transform (C-CSHT) is a variant of complex Hadamard transform and effective for some signal processing and communication applications. Its closed-form factorization of the general N-channel (N = 2m) case was recently proposed, however, there still exist a room to find an effective factorization especially for unified factorization of C-CSHT and its real-valued transform counterpart (R-CSHT). In this paper, we present another simple closed-form factorization of C-CSHT based on that of R-CSHT. The proposed factorization is applicable for both complex- and real-valued CSHTs with one factorization. Furthermore, the relationship with the common block transform, DCT, is revealed.

In this paper, we propose the improved seam merging method for content-aware image resizing. This method merges a two-pixel-width seam element into one new pixel in image reduction and inserts a new pixel between the two pixels in image enlargement. To preserve important contents and structure, our method uses importance and structure energies. Using the cartoon image of an original image for calculation of structure energy, our method can preserve main structure. In addition, we introduce new energy to suppress distortion generated by excessive reduction or enlargement in the iterative merging or inserting. Experimental results demonstrate that the proposed method can produce satisfactory results in both image reduction and enlargement.

Discrete cosine transform (DCT) is known as efficient frequency transform, and when it is implemented on software/hardware, multiplier is undesirable for faster implementation. This paper presents a realization of multiplierless fast DCT for lossy image/video coding on arbitrary devices. First, the proposed DCT is constructed by using fast Hartley transform (FHT). Next, the redundancy of the structure is eliminated by using several characteristics of rotation matrix. Then, multiplierless DCT is obtained by approximating rotation matrices to multiplierless lifting structures with adders and bit-shifters. Finally, the proposed DCT is validated by comparing with the conventional DCTs in image coding.

We proposed a novel method for content-aware image resizing based on grid transformation. Our method moves each vertical and horizontal grid lines in the perpendicular direction to itself. Keeping important regions unchanged is a strong constraint for image resizing. Satisfying this constraint can produce significant distortion on unimportant regions. Our method allows important regions to be changed and suppresses the changes of the aspect ratios of important regions. In addition, we introduced the lower thresholds of the scaling rates of grid meshes and the boundary discarding process. Experimental results demonstrate that our proposed method resizes images with less distortion than other resizing methods.

This paper presents an effective signal boundary solution in lossy-to-lossless image coding which is the unification of lossy and lossless image coding. Although M-channel filter banks (FBs) for lossy image coding have several effective signal boundary solutions, M-channel lifting based FBs (L-FBs) for lossless image coding do not have such an effective signal boundary solutions due to rounding error in each lifting step. This paper proposes reversible non-expansive symmetric convolution for M-channel lifting based linear-phase FBs (L-LPFBs) to apply lossy-to-lossless image coding. Our proposal is validated by comparing with the periodic extension in lossy-to-lossless image coding.

This paper proposes an image coding method incorporated with content-aware image resizing. It is a promising application of our previously proposed rate-dependent seam carving (RD-SC). RD-SC is combined with lifting-based discrete wavelet transform to construct a new multiresolution image representation. Furthermore, the modified parent-children relationship of SPIHT is shown. Our proposed image coding presents comparable performances to the conventional SPIHT even for the original size, and retargeted image quality is satisfactory.

Generalized block-lifting factorization of M-channel (M > 2) biorthogonal filter banks (BOFBs) for lossy-to-lossless image coding is presented in this paper. Since the proposed block-lifting structure is more general than the conventional lifting factorizations and does NOT require many restrictions such as paraunitary, number of channels, and McMillan degree in each building block unlike the conventional lifting factorizations, its coding gain is higher than that of the previous methods. Several proposed BOFBs are designed and applied to image coding. Comparing the results with conventional lossy-to-lossless image coding structures, including the 5/3- and 9/7-tap discrete wavelet transforms in JPEG 2000 and a 4 × 8 hierarchical lapped biorthogonal transform in JPEG XR, the proposed BOFBs achieve better result in both objective measure and perceptual visual quality for the images with a lot of high-frequency components.

In image resizing process, preserving structure on an image is important to produce plausible results. We proposed seam merging, a seam-carving-based image resizing method, and a new energy criterion for structure preservation. Seam merging reduces the size of an image by merging a two-pixel-width seam into a one-pixel width seam. To find the optimal seam that minimizes structural distortion after merging, we introduce an energy function which has a large value when the merging breaks the structure. We further show the way to find the optimal seam using dynamic programming. Experimental results demonstrate that our proposal algorithm can produce fewer artifacts and successfully preserve structure.

Integer lapped orthogonal transforms (LOTs) are vital technologies for the unification of lossless and lossy image coding, called lossless to-lossy image coding. In this paper, we present an efficient realization of integer fast LOT (FLOT) based on direct-lifting of discrete cosine transforms (DCTs) which are type-II, III and IV. Although the conventional integer FLOTs suffer from degradation of coding performance due to much rounding error generated by cascading lifting structures, this paper presents a realization of a simpler, faster and more efficient transform with only some adders, 1-bit shifters and direct use of DCTs for lifting coefficients. As result, the proposed method is validated in lossless-to-lossy image coding.

In this paper, we propose a two dimensional (2D) non-separable adaptive directional lifting (ADL) structure of discrete wavelet trans form (DWT) and its image coding application. Conventionally, we have proposed a polyphase representation of a 2D non-separable lifting structure of DWT. We generalize the polyphase representation in this paper and one structure of the class has been proven to reduce errors due to the rounding operations and improve a compatibility of the irreversible 9/7 DWT, compared with a 2D separable lifting structure of DWT. Adding the adaptive directional transforming property to the generalized structure, our proposed method improves the lossy image coding performance with maintaining the compatibility.

Content aware image resizing technique has become more important with the development of device technology. Although the seam carving method produces high-quality resized images, it requires high computational complexity. In this paper, we propose a faster content-aware image resizing technique. Our method performs seam carving in wavelet transform domain. This approach reduces the computational complexity of image resizing. To avoid breaking in the spatial continuity of an image, our method reduces the image width by scaling a seam width down instead of carving it out. In addition, the decomposition level can be decreased adaptively to avoid distortion. We show our method produces resized images with less distortion and less computational cost than the seam carving method.

In the dark place photographing, the increase of noise is one of the major problems to be addressed. Although using a flash is effective to reduce the noise, natural colors are faded away due to increase of specular lights. In this paper, we present a method that generates a no-flash like flash image by approximating colors of a flash image by those of a no-flash image. Our method is based on the ”color-line” feature of images, a linear distribution of colors in a local region is transformed by a set of transform matrices automatically. This method is able to deal correctly with the occluded regions where the colors are saturated by reflections or shadows and the color distribution is squashed.

A block-lifting factorization of M-channel biorthogonal filter banks (BOFBs) with degree-N building blocks and even/odd M (M ≥ 2) for lossless-to-lossy image coding is introduced in this paper. In the previous work, block-lifting factorization of M-channel BOFBs has been proposed. Since the block-lifting structure does not require the restriction of determinant of each building block, it achieves better coding performance than the conventional methods. However, the factorization is not completed because McMillan degree in each building block is fixed M/2 (M is even). This paper proposes a block-lifting factorization without restrictions for a fixed degree and even block size. Our proposal is validated by several filter designs and their application to lossless-to-lossy image coding.

In this paper, a novel direction-adaptive image coding scheme is introduced by using two-dimensional adaptive directional lifting-based wavelet transform (2D-ADLWT). Conventionally, one-dimensional ADLWT (1D-ADLWT) has been proposed. However, it requires large amount of computational cost for optimal lifting direction decision and image transformation. In this work, adaptive directional lifting is implemented by using 2D direct lifting wavelet transform and directional downsampling matrices. Direct 2D lifting structure can reduce the computational cost for image transformation and optimal lifting direction decision significantly. Moreover, in the simulation, it is shown that the proposed method is comparable to the 1D-ADLWT in terms of image coding efficiency. Thus, an effective ADLWT with low computational cost can be provided.

Some adaptive image interpolation methods have been proposed to create higher visual quality images than traditional interpolation methods such as bicubic interpolation. These methods, however, often suffer from high computational costs and unnatural texture interpolation. This paper proposes a novel edge-adaptive image interpolation method using an edge-directed smoothness filter. Our approach estimates the enlarged image from the original image based on an observation model. The estimated image is constrained to have many edge-directed smooth pixels which are measured by using the edge-directed smoothness filter introduced in this paper. Simulation results show that the proposal method produces images with higher visual quality, higher PSNRs and faster computational times than the conventional methods.

A discrete cosine transform (DCT) can be easily implemented in software and hardware for the JPEG and MPEG formats. Recently, some integer DCTs (IntDCTs) for lossless-to-lossy image coding have been proposed, but they do not satisfy enough compatibility with JPEG standard. This paper proposes a realization of lossless-to-lossy image coding which has higher compatibility with it than the conventional IntDCTs. Our IntDCT is implemented by direct-lifting of DCT and inverse DCT (IDCT) and has high performance in lossless image coding compared with any IntDCT while keeping high compatibility with JPEG standard. Finally, our method is validated by its application to lossless-to-lossy image coding.

In this paper, we propose a lattice structure of two-dimensional (2-D) linear-phase paraunitary filter banks (LPPUFBs) called as 2-D GenLOT. Muramatsu et al. have proposed a lattice structure of 2-D LPPUFBs conventionally. Our 2-D GenLOTs save design parameters and computational costs compared to the conventional 2-D LPPUFBs. We impose the regularity condition on the proposed FBs for image coding application. The 2-D GenLOTs perform an efficient image coding application.

This paper presents an IntDCT with only dyadic values such as k/2n(k, n ∈ N). Although some IntDCTs have been proposed, they are unsuitable for lossless-to-lossy image coding in low-bit-word-length (coefficients). First, the proposed M-channel lossless WHT (LWHT) can be constructed by only (log2M)-bit-word-length and has structural regularity. Then, our 8-channel IntDCT keeps good coding performance even In low-bit-word-length because LWHT, which is main part of IntDCT, can be implemented by 3-bit-word-length. Finally, our method is validated In lossless-to-lossy image coding.

Adaptive directional wavelet transform is an effective alternative of the traditional 2-D wavelet transform for image coding. It is able to transform an image adaptively along diagonal orientations as well as conventional vertical/horizontal directions. However, it requires to transmit transform direction information to the decoder side. For image coding at very low bitrates, the bit budget of the direction information degrades a reconstructed image quality. In this paper, a method to construct a scalable bitstream for transform directions is presented. We utilize the fact that the matrix yielded by transform direction indices still contains the original image characteristics. The matrix is transformed by a block-lifting based DCT, then encoded by SPIHT to yield a scalable bitstream. Our method is effective for very low bitrate image coding, and is comparable to the non-scalable one for middle-to-high bitrates.

A discrete cosine transform (DCT) can be easily implemented in software and hardware for the JPEG and MPEG formats. However, even though some integer DCTs (IntDCTs) for lossless-to-lossy image coding have been proposed, such transform requires redesigned devices. This paper proposes a hardware-friendly IntDCT that can be applied to both lossless and lossy coding. Our IntDCT is implemented by direct-lifting of DCT and inverse DCT (IDCT). Consequently, any existing DCT device can be directly applied to every lifting block. Although our method requires a small side information block (SIB), it is validated by its application to lossless-to-lossy image coding.

This paper proposes an efficient approach for adaptive directional wavelet transform (WT) based on directional prefiltering. Although the adaptive directional WT is able to transform an image along diagonal orientations as well as traditional horizontal and vertical directions, it sacrifices computation speed for good image coding performance. We present two efficient methods to find the best transform directions by prefiltering using 2-D filter bank or 1-D directional WT along two fixed directions. The proposed direction calculation methods achieve comparable image coding performance comparing to the conventional one with less complexity. Furthermore, transform direction data of the proposed method can be used for content-based image retrieval to increase retrieval ratio.

This paper proposes a computationally efficient approach of adaptive directional wavelet transform (AD WT). The AD WT is based on lifting implementation of WT, and it is able to transform an image along diagonal orientations as well as traditional horizontal and vertical directions. The AD WT sacrifices computational speed for its good image coding performance. We present an alternative method to find the best transform directions by pre-directional filterings for the AD WT. The proposed direction calculation method shows very comparable image coding performance to the conventional one, whereas its computational cost is relatively very low.

The purpose of this paper is to show an another design approach of the M-band dual-tree complex wavelet transform (DTCopfWT). Conventionally, M-channel cosine-sine modulated filter bank has been proposed as an extension of cosine modulated filter bank. It can be easily designed by the modulation of one prototype filter. In this paper, we show that it can be regarded as an alternative DTCopfWT with respect to its relationship to the analyticity. In addition, we also present its shift-invariance, rich directional selectivity which are effective for the image processing. Therefore it can provide the simple design of M-band DTCopfWT. In this paper, these properties are verified by theoretical analysis and demonstrations.

In this paper, we propose an extension of combined 2D and 1D-directional filter banks (TODFBs) with adaptive approach in their 1D-directional stages. TODFBs show better performance in image coding and denoising compared to the traditional wavelet transform (WT), however, they still have possibilities to improve their performance in image coding by adopting the adaptive directional WTs for their 1D-directional stages. An efficient method to determine the transform directions is also proposed. In image coding results, our proposed filter banks gain PSNR and visual quality improvements compared with the WTs and the non-adaptive TODFBs.

In this paper, effective multiresolution image representations using a combination of 2-D filter bank (FB) and directional wavelet transform (WT) are presented. The proposed methods yield simple implementation and low computation costs compared to previous 1-D and 2-D FB combinations or adaptive directional WT methods. Furthermore, they are nonredundant transforms and realize quad-tree like multiresolution representations. In applications on nonlinear approximation, image coding, and denoising, the proposed filter banks show visual quality improvements and have higher PSNR than the conventional separable WT or the contourlet.

In this paper, a novel design method of critically sampled contourlet transform (CSCT) is proposed. Although, several types of CSCT have been proposed, they have some problems on efficiency and flexibility of their frequency plane partition patterns. In contrast to the way in conventional design methods based on a "top-down" approach, the proposed one is based on a "bottom-up" one. That is, the proposed CSCT decomposes the frequency plane into small directional sub- bands, and then synthesizes them up to a target frequency plane partition, while the conventional ones decompose into it directly. By this way, the proposed CSCT can provide an efficient and flexible frequency plane partition for image coding.

In this paper, an effective multiresolution image representation using the combination of 2D quincunx filter bank (FB) and directional wavelet transform (WT) is presented. The proposed method yields simple implementation and low calculation costs compared to the other 1D and 2D FB combinations or adaptive directional WTs. Furthermore, it is a nonredundant transform and realizes quad-tree like multiresolution representation. In applications on nonlinear approximation and image coding, the proposed filter bank shows visual quality improvements and has higher PSNR.

This paper proposes new building blocks for the lattice structure of oversampled linear-phase perfect reconstruction filter banks (OLPPRFBs). The structure is an extended version of higher-order feasible building blocks for critically-sampled LPPRFBs. It uses fewer number of building blocks and design parameters than those of traditional OLPPRFBs, whereas the frequency characteristic of the new OLPPRFB is comparable to that of traditional one.

In this paper, we propose the client-server system which accomplishes acquisition, transmission and reconstruction of the 3D shape at a remote location in real time. The server consists of stereo cameras and a PC cluster, in which each PC creates a range image using multiple color images obtained from the stereo cameras connected to it. All PCs on the server side work in synchronization and generate range images in parallel with each other, which are then transmitted to the client as a point cloud. On the client side, the 3D model is reconstructed using a received point cloud by the point-based rendering method. We propose the cylindrical mapping method, which removes overlaps and annoying artifacts efficiently before the rendering process. All the procedure of generation, transmission, and reconstruction of successive range images is done in real time.

This paper introduces an image transform method by using M-channel biorthogonal filter banks (BOFBs) with an efficient lifting factorization. The proposed lifting factorization of a building block in their lattice structure has unity diagonal scaling coefficients and guarantees perfect reconstruction even if the obtained coefficients are quantized. Since the number of rounding operators of proposed lifting-based BOFBs (LBBOFBs) can be reduced by merging the lifting steps, the proposed structure is efficient for lossless image coding. Image coding results indicate better performance than conventional methods.

In this paper, we present the structure and design method for a first-order linear-phase filter bank (FOLPFB) which has unequal filter lengths in its synthesis bank (UFLPFB). A FOLPFB is a generalized version of biorthogonal LPFBs regarding their synthesis filter lengths. Ringing artifact is the main disadvantage of image coding based on FOLPFBs. UFLPFBs can reduce the ringing artifacts as well as approximate smooth regions well.

In recent years, two-channel complex-valued filterbanks have been studied and found theirs several important applications by many researchers, such as complex signal and image processing. One of those important results is that there is no two-channel complex-valued linear-phase paraunitary filterbank (CLPPUFB), except for its filter lengths of 2. In this paper, we introduce a class of special complex-valued filterbanks which is a subclass of biorthogonal filterbanks. Those filterbanks are called complex pseudo-orthogonal filterbanks (CPOFB), based on the concept of pseudo-orthogonality (PO). This kind of orthogonality, we propose, is different from the conventional one essentially. This paper also shows possibility to design a two-channel complex linear-phase filterbank (CLPFB) with its filter lengths are more than 2, based on PO. Finally, we show a design example of a complex linear-phase pseudo-orthogonal filterbank (CLPPOFB). Moreover, such CPOFB can satisfy the linear-phase condition simultaneously with filter lengths are more than 2. This paper shows a theory, a design method and an example of CLPPOFB

In this paper, we present a novel lattice structure and design of the linear phase M-channel paraunitary filter banks whose filters all have zeros at the mirror frequencies except for the passband. This structure is implemented by replacing the first block of the lattice structure with two type II DCTs. With this structure, the filter banks are implemented with high speed and are designed without taking account of the stopband attenuation. Finally, we show some examples to validate the proposed method.

The paper presents a study on similarity detection of different 3D meshes. Our method consists of three steps. First, 3D meshes are aligned by PCA such that all of them have a same principal axis. Each rotated surface is approximated by a deformed cylinder with regular grids. Then we compare the distances by calculating their correlation. These steps are done in a hierarchical fashion. We demonstrate with examples that the proposed method can detect the similarity precisely and easily.

This paper describes fast registration approaches of range images based on their multiresolution representations. In the iterative closest point algorithm, which is a popular technique to register sets of 3D points, the computational complexity depends largely on the number of points representing range image. Therefore, we accelerate a range image registration by applying shape-adaptive discrete wavelet transform to range images and efficiently reducing the number of data points. In addition, we present a fast and accurate registration method, which finds the closest point to a given point hierarchically in consideration of the wavelet decomposition. Finally, we apply these techniques to the registration of actual range images and show the validity of the proposed approaches.

In this letter, a parallel analog-digital (A/D) conversion scheme with a filter bank for low intermediate-frequency receivers is presented. The analysis filters of the filter bank divide the frequency components of the received signal, and achieve parallel A/D conversion. Therefore, the required conversion rates and the resolution of the A/D converters can be reduced and the receiver can demodulate wideband signals. As the analysis filters consist of analog components, their coefficients include errors. These errors cause mutual interference between signals in orthogonal frequencies. In order to remove this interference, a decorrelating compensation scheme is proposed.

In this paper, we present a new design method of allpass digital filters with equiripple group delay response. This method is based on solving a least squares solution iteratively. At each iteration, the desired group delay response is transformed so as to have equiripple error. By this method, an equiripple solution is obtained very quickly with less computational complexity.

In transform-based image coding, the periodic extension has the disadvantage that it might introduce high frequency components due to the artificial discontinuities at the signal boundaries. On the other hand, the symmetric extension cannot be applied to the two-channel orthogonal filter bank because linear phase is not possible. This paper describes a smooth extension method, which provides the symmetric decimated outputs of the analysis filters at the boundary, for the two-channel orthogonal filter bank to obtain nonexpansive subband signals. In our approach, the extended signal has the flexibility and we calculate the smooth one by singular value decomposition. Finally, several image coding and extended signal examples are shown to confirm the validity of the proposed approach.

In the transform-based image coding, the symmetric extension is important to obtain subband signals effectively without increasing the total number of signal. However in the case of the symmetric extension, subband filters have to be (anti-)symmetric. This means that the linear phase property is strict constraint on filters' impulse response for the symmetric extension. For the other method of the signal extension, the periodic extension is implemented. While it can be applied to any filters, it introduces artificial discontinuities at the signal boundaries. In this paper, we present a smooth extension for M-channel filterbanks to implement nonexpansive decomposition. First, we derive a condition for solving the coefficient expansion problem. Second, we calculate a smooth extended signal under the condition by singular value decomposition. Finally, we design 8 channel 16 tap paraunitary filterbank using lattice structure, and several image coding and extended signal examples are shown to confirm the validity of the proposed approach.

This paper describes a lattice structure and a design for orthogonal and biorthogonal multiwavelets. First, we factorize the polyphase matrices of symmetric-antisymmetric multifilter bank into elementary low-order building blocks. Second, we transform a tree-structured multiwavelet system into an equivalent scalar filter bank in order to design optimal multifilter banks. Simulation results show that the proposed orthogonal and biorthogonal multiwavelets have superior performance to the popular multiwavelet SA4 and the (9,7)-tap scalar wavelet.

We describe a new video coding scheme using filter bank and subband motion estimation and compensation. Inmost of video coding schemes such as MPEG [2], they have problem of blocking artifacts and computational complexity in motion estimation. We use Lapped Biorthogonal Transform (LBT) instead of DCT to reduce the blocking artifacts, and use the motion estimation in subband block domain to reduce the computational complexity. Intra-frames and the difference frames between the current and predicted frames in a video sequence are encoded by Efficient Embedded Zerotree Wavelet codec (EEZW) [7]. They permit scalability, progressive transmission, and exact bit-rate control.

In this paper, we present the theory, design and imple-mentation of generalized linear-phase paraunitary nonuni-form filter bank (GenLPPUNUFB). Tree structure of wavelet transform is regarded as nonuniform filter bank (NUFB), and it will be adopted in JPEG2000 which will become the next standard for still image coding. However 2-channel linear-phase paraunitary NUFB (LPPUNUFB) does not exist except for Haar function, so it isn't optimal in the sense of transform coding gain. Although direct structured LPPUNUFB, which overcomes tree structured LPPUNUFB (Haar function), has already been presented [3], it is not general. Therefore we develop lattice structure of GenLPPUNUFB, and we show some examples and confirm the validity of our method.

Wavelet packets represent an elegant generalization of the wavelet transform, capable of providing arbitrary frequency resolution to meet a signal's spectral behaviors. Recent research advances have shown that wavelet-based image compression techniques offer several advantages over traditional techniques in terms of progressive transmission capability and compression efficiency. The embedded compression techniques - tree-structured coding techniques, such as embedded zerotree wavelet (EZW) and set partitioning in hierarchical trees (SPIRT), and quadtree-structured coding techniques, such as wavelet quadtree (WQT), multigrid embedded (MGE) and EZW based on intraband partitioning (EZW-IP), - demonstrate the competitive performance of wavelet based compression schemes. This paper describes the wavelet packet algorithm which makes it suited to subsequent quad tree-based embedded image coders, such as EZW-IP. In our technique, the hierarchical sums of maximum magnitude of each quadtree node role as the decomposition criterion. The simulation results for various images show that the proposed algorithm gives a better coding efficiency than the octave-band decomposition.

In this paper, a novel method of the surface reconstruction from a single monocular image is proposed. Our proposed approach (called shape from knowledge) is based on the knowledge of objects, which is acquired by learning from a number of samples. To achieve this, we investigate making use of the hidden Markov model (HMM) framework, which models the correspondence between an intensity image an its depth information. We have applied our algorithm to the 3-D face and 3-D hand reconstruction from single images, and the results show the effectiveness of the proposed method.

Due to the rapid development of computer and information technology, 3D modeling and rendering capabilities are becoming increasingly important in many applications, including industrial design, architecture, CAD/CAM, video games, and medical imaging. Since 3D mesh models often have the huge amount of the data, it is time-consuming to retrieve from a storage device or to download from the network. Most 3D viewing applications need to obtain the entire file of a 3D model in order to display the model, even when the user is interested only in a low-resolution version of the model. Therefore, progressive coding that enables multiresolution transmission of 3D models is desired. We propose the progressive coding scheme of 3D meshes with texture, in which we convert irregular meshes to semiregular using texture coordinates, map them on planes, and apply 2D image coding algorithm to mesh compression. As our method uses the wavelet transform, the encoded bitstream has a progressive nature. We gain high compression rate with the same visual quality as original models.

A digital compensation scheme for coefficient errors of a complex filter bank in low-IF receivers is presented. The complex filter bank is employed to suppress DC offset and image signals in the low-IF receivers and relax the requirements on the conversion rate and resolution of A/D converters. The proposed compensation scheme regenerates interference due to the coefficient errors and subtracts it from the digital signal converted by an A/D converter. The proposed scheme also improves the effective resolution of A/D converters.

In general, highly detailed 3D meshes are often large and time-consuming to download. In order to address the problem, the amount of 3D data is reduced by decimating triangles which has little influence on visual quality. However, since few schemes for quantitative evaluation have been established yet, subjective evaluation is often used. While 1D and 2D digital signals exist only on sampling points, there are no "sampling points" in 3D meshes which makes it difficult to evaluate the differences of two meshes. A computational scheme to measure the error between two meshes is proposed. The error is measured by dividing 3D meshes into some 2D planes and then further segmenting the 2D planes to pixels. Our algorithm handles not only the geometric error but also color differences.

In this paper, generalized linear phase lapped orthogonal transforms with unequal length basis functions (GULLOT) are considered. The length of each basis of the proposed GULLOT can be different from each other, while all the bases of the conventional GenLOT are of equal length. In order to apply the GULLOT to subband image coding, we also investigate the size-limited structure to process the finite length signal which is important in practice.

We present a design and implementation of M-channel linear-phase paraunitary filter banks (LPPUFB) with unequal length filters and same center points. Our main motivation is the application in effective image coding. For low-frequency signals, long basis functions should be used to avoid the blocking effect. While, short basis functions should be used to reduce the ringing noise for high-frequency signals. LPPUFB with such characteristics can be achieved structurally by taking account of the lattice structure. Finally some design examples are shown.

It has been proposed that resolution progressiveness is one of the most important techniques for image compression. In this paper, we offer a new resolution progressive coding method. The main point stresses how to exploit self-similarity across different scales of wavelet transform by sorting the coefficients. Wavelet transformed images inherently have correlation between subbands at different levels in a spatial decomposition hierarchy, and thus exploiting the correlation of the hierarchy helps to compress the amount of information of images. A number of methods with SNR progressive coding have been presented so far; however, this proposed method concerns resolution progressiveness as well as SNR progressiveness, which can be only applied in each subband, and still be effective and computationally very simple for image compression.

In this paper, we propose a design of FIR filters with equiripple magnitude and phase responses in complex domain. In every iteration, we use a transformed error response as an ideal frequency response. Since the proposed method does not require any optimization procedure, it can significantly reduce the amount of computation.

Most natural images are well modeled as smoothed areas segmented by edges. The smooth areas can be well represented by a wavelet transform with high regularity and with fewer coefficients which requires high-pass filters with some vanishing moments. However for the regions around edges, short highpass filters are preferable. In one recently proposed approach, this problem was solved by switching filter banks using longer filters for smoothed areas of the images and shorter filters for areas with edges. This approach was applied to lossy image coding resulting in a reduction of ringing artifacts. As edges were predicted using neighboring pixels the nonlinear transforms made the decorrelation more flexible. In this paper we propose a time-varying filterbank and apply it to lossless image coding. In this scheme, we estimate the standard deviation of the neighboring pixels of the current pixel by solving the maximum likelihood problem. The filterbank is switched between three filter banks, depending on the estimated standard deviation.

In this paper, we present optimal nonuniform lapped biorthogonal transforms for image compression. Subband coding using wavelet transforms have received a lot of attention because of multiresolution representation. The wavelet transform is regarded as a nonuniform filter bank and is constructed using the tree structure of a two-channel filter bank. However, it may not be optimal in the sense of energy compaction. If we can design nonuniform filter banks directly, it is possible to overcome the conventional wavelet transform. We then design a direct-structured nonuniform filter bank with a lapping window, called NULBT. Finally we show some examples and confirm the validity of our method.

In this paper, we focus on two-channel perfect reconstruction IIR filter banks. Often two-channel FIR filter banks with additional characteristics such as the perfect reconstruction property and linear phase are used in subband systems. This type of filter banks belongs to the class called biorthogonal filter banks. While several works have pointed out that the perfect reconstruction IIR filter banks have both linear phase and orthogonality, the linear phase orthogonal IIR filter banks have never been applied to image coding. Then we apply the two-channel perfect reconstruction IIR filter banks consisted of allpass filters, with both linear phase and orthogonality, to image coding and show that the proposed IIR filter bank with 3 zeros at z=1 for the analysis lowpass filter, has less computational complexity and produces better results in terms of PSNR than the FIR filter bank, namely the two-channel linear phase biorthogonal (9,7)-taps. Consequently both linear phase and orthogonality are essential to improve coding performance.

Block orthogonal transforms (BOTs) are commonly used for lots of applications. Conventional BOTs are based on uniform filter banks, however, nonuniform BOTs are often superior to uniform ones. In this research, we investigate the factorization of nonuniform BOTs which does not involve the tree structure. Therefore, optimal nonuniform BOTs are available in the sense of transform coding gain. Some design examples are included to confirm our theory. We also apply the nonuniform BOT to the transform image coding.

Since IIR filters have lower computational complexity than FIR filters, some design methods for IIR filter banks have been presented in the recent literature. Smith et al. (1990) have proposed a class of linear phase IIR filter banks. However this method restricts the order of the numerator to be odd and, moreover, has some drawbacks. In this paper we present two design methods for linear phase IIR filter banks. One is based on Lagrange-Multiplier method, in which optimal IIR filter banks in least squares sense are obtained. In the other approach, IIR filter banks with the maximum number of zeros are derived analytically.

We present a novel way to design biorthogonal and paraunitary linear phase (LPPUFB) filter banks. The square error of the perfect reconstruction condition is expressed in a quadratic form of filter coefficients and the cost function is minimized by solving the linear equation iteratively without nonlinear optimization. With some modifications, the method can be extended to the design of paraunitary filter banks. Using this method, we can design LPPUFB with many channels easily and quickly. Design examples are given to validate the proposed method.

In this research, we propose a direct design method of nonuniform filter banks (NUFBs). This method is based on frequency domain constraints to eliminate the amplitude and the aliasing distortions. Both NUFBs with integer and rational sampling factors can be designed with a common procedure. Here, we also consider the design method which requires only to solve linear equations iteratively. In our proposed method, least square errors of the perfect reconstruction (PR) constraints are minimized without using the nonlinear programming technique.

This paper presents the theory, design, and efficient implementation of a new class of linear phase paraunitary filter banks (LPPUFB) which find application in transform-based image coding. These new LPPUFB have filters of different lengths: longer filters are kept for low-frequency components to prevent blocking, while shorter filters are reserved for high-frequency components to minimize ringing. The proposed lattice factorization structurally enforces the unequal-length property along with LP and PU properties, and it is robust under the quantization of lattice coefficients. Design and image coding examples are also presented to confirm the validity of the theory.

We present a design method of 2-dimensional (2D) linear phase (LP) perfect reconstruction (PR) FIR filter banks based on the Lagrange multiplier method. In M analysis filters, we first design M-1 analysis filters which have an LP property. Finally we design the Mth analysis filter with LP so that the overall system satisfy PR. Then the Mth analysis filter is optimized to have a good response while keeping PR based on the Lagrange multiplier method. By this method, 2D LP PR filter banks can be easily designed by only solving the simultaneous equation, although the order of the Mth analysis filter is higher than that of the others.

In this paper, we propose a design method of cosine-modulated 2-dimensional (2-D) perfect reconstruction (PR) FIR filter banks, in which each analysis and synthesis filter has linear phase (LP). As in previous works, it is impossible to design the 2-D cosine modulated system which satisfies both the PR condition and LP property. However, in 2-D signal processing, it is very important for each filter to have the LP property. Our main goals are to show such a system can be realized by considering a new decomposition scheme and derive the conditions for PR and LP. A design example is included to show the effectiveness of this paper.

In this paper, the author considers the theory of modulated 2 dimensional (2-D) perfect reconstruction (PR) filter banks with permissible passbands. At first, the author designs a 2-D complex digital filter with half passband obtained by the sampling matrix. Next, 2-D analysis filter banks are realized by modulating this prototype 2-D complex digital filter and by taking the real part of the output. It is also shown that the modulation in the 2-D frequency plane is equivalent to a 1-D DFT. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. Finally, some examples are shown.

In this paper, we present a design method of 2 dimensional (2-D) perfect reconstruction (PR) filter banks with permissible passbands by modulating a complex prototype 2-D FIR digital filter. At first, we design a 2-D complex digital filter with half of a passband obtained by a sampling matrix. Then, we show that the 2-D analysis filter banks can be realized by modulating this prototype 2-D complex digital filter and taking the real part of the output. It is demonstrated that the modulation in 2-D frequency plane is equivalent to one dimensional (1-D) discrete-Fourier-transform (DFT). We also derive a necessary and sufficient condition for the 2-D PR filter banks.

Considers the theory of cosine-modulated 2 dimensional (2-D) perfect reconstruction (PR) filter banks. First, a 2-D digital filter design with half passband, obtained by the sampling matrix, is discussed. Next, 2-D analysis filter banks are realized by cosine-modulating this prototype 2-D digital filter. It is shown that the modulation in the 2-D frequency plane is equivalent to the 1-D modulation. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. If the polyphase filter pairs of the prototype filter have a double-complement, the resulting 2-D filter bank satisfies the condition of perfect reconstruction.>

The design of a 2-dimensional (2-D) recursive orthogonal wavelet based on iterated filter banks is investigated. To obtain the orthogonal wavelet, we use the parallel connection of some delays and a 2-D allpass filter. In this case, a pair of digital filters with orthogonality is obtained structurally and digital filters with arbitrarily orders can be designed. Furthermore a maximum number of zeros is put at aliasing frequencies in the lowpass filter to obtain the regularity of the wavelet. Design examples of discrete scaling and wavelet functions are presented.>

It is well known that FIR filter banks, satisfying the perfect reconstruction (PR) property, can be obtained by cosine modulation of linear-phase prototype FIR digital filter. In this paper, it is shown to be possible to design 2-dimensional (2-D) PR filter banks using cosine modulation as for the 1-D case. At first, the author designs a 2-D digital filter with half passband obtained by the sampling matrix. Next, 2-D analysis filter banks are realized by cosine-modulating this prototype 2-D digital filter. It is shown that the modulation in 2-D frequency plane is equivalent to the 1-D modulation. A necessary and sufficient condition for 2-D perfect reconstruction filter banks is derived. Furthermore the author formulates the design method as a quadratic-constrained least-square minimization problem.>