We propose a Weakly Supervised Object Localization (WSOL) method that can locate an object within a given image using a pre-trained network learned with only class labels without location annotations. Most existing WSOL methods rely on thresholding a Class Activation Map (CAM) generated by the pre-trained network to highlight and localize the object. However such approaches often produce incomplete object bounding boxes, as only the discriminative parts of the object are selected during thresholding. We revisit current CAM-based WSOL approaches and propose a pipeline to: (1) refine the CAM map using Weighted Global Average Pooling (WGAP), (2) recombine weights to make use of the negative features, (3) adaptively select a suitable threshold to achieve better object localization. Our method does not require additional learning or hyperparameter tuning. We show that our simple approach can achieve competitive results when evaluated on the CUB-200-2011 and ILSVRC 2016 datasets against other state-of-the-art methods.

The research in automatic unsupervised visual clustering has received considerable attention over the last couple years. It aims at explaining distributions of unlabeled visual images by clustering them via a parameterized model of appearance. Graph Convolutional Neural Networks (GCN) have recently been one of the most popular clustering methods. However, it has reached some limitations. Firstly, it is quite sensitive to hard or noisy samples. Secondly, it is hard to investigate with various deep network models due to its computational training time. Finally, it is hard to design an end-to-end training model between the deep feature extraction and GCN clustering modeling. This work therefore presents the Clusformer, a simple but new perspective of Transformer based approach, to automatic visual clustering via its unsupervised attention mechanism. The proposed method is able to robustly deal with noisy or hard samples. It is also flexible and effective to collaborate with different deep network models with various model sizes in an end-to-end framework. The proposed method is evaluated on two popular large-scale visual databases, i.e. Google Landmark and MS-Celeb1M face database, and outperforms prior unsupervised clustering methods. Code will be available at https://github.com/VinAIResearch/Clusformer

In this paper, we propose an approach to automate the process of place name detection in the medical domain to enable epidemiologists to better study and model the spread of viruses.We created a family of Toponym Identification Models based on BERT (TIMBERT), in order to learn in an end-to-end fashion the mapping from an input sentence to the associated sentence labeled with toponyms.When evaluated with the SemEval 2019 task 12 test set (Weissenbacher et al., 2019), our best TIMBERT model achieves an F1 score of 90.85%, a significant improvement compared to the state-of-the-art of 89.

The age of social media insists on developing devices that are able to capture and share ones' moments with high fidelity. Handheld devices such as smartphones with wide-angle cameras have shown the current trend in mobile photography. Although one can take great delight in a wide field of view through modern cameras, nearby objects or faces may be distorted significantly. Recent works have obtained impressive results in this research area, but there is still a tradeoff between image quality and processing time to consider. This work introduces an adaptive polynomial model that automatically selects faces and performs image distortion correction. Since the photos are processed locally, faces are undistorted, and the background is close to the original state. Unlike other content-aware based methods which rely on heavy computing components and high image resolution, our model is suitable for mobile devices to tackle face distortion issue in selfie photos.

Weakly Supervised Object Localization (WSOL) task aims to recognize the object position by using only image-level labels. Some previous techniques remove the most discriminative parts for all input images or random images to capture the entire object location. However, these methods can not perform the correct operation on different images such as hiding the data or feature maps that should not be hidden. In this case, both classification and localization accuracy will be affected. Meanwhile, just erasing the most important regions tends to make the model learn the less discriminative parts from outside of the objects. To address these limitations, we propose an Attention-based Selection Strategy (ASS) method to choose images that do need to be erased. Moreover, we use different threshold self-attention maps to reduce the impact of unhelpful information in one of the branches of our selection strategy. Based on our experiments, the proposed method is simple but effective to improve the performance of WSOL. In particular, ASS achieves new state-of-the-art accuracy on CUB-200-2011 dataset and works very well on ILSVRC 2016 dataset.

This paper presents a novel approach for synthesizing automatically age-progressed facial images in video sequences using Deep Reinforcement Learning. The proposed method models facial structures and the longitudinal face-aging process of given subjects coherently across video frames. The approach is optimized using a long-term reward, Reinforcement Learning function with deep feature extraction from Deep Convolutional Neural Network. Unlike previous age-progression methods that are only able to synthesize an aged likeness of a face from a single input image, the proposed approach is capable of age-progressing facial likenesses in videos with consistently synthesized facial features across frames. In addition, the deep reinforcement learning method guarantees preservation of the visual identity of input faces after age-progression. Results on videos of our new collected aging face AGFW-v2 database demonstrate the advantages of the proposed solution in terms of both quality of age-progressed faces, temporal smoothness, and cross-age face verification.

Although widely used, Multilinear PCA (MPCA), one of the leading multilinear analysis methods, still suffers from four major drawbacks. First, it is very sensitive to outliers and noise. Second, it is unable to cope with missing values. Third, it is computationally expensive since MPCA deals with large multi-dimensional datasets. Finally, it is unable to maintain the local geometrical structures due to the averaging process. This paper proposes a novel approach named Compressed Submanifold Multifactor Analysis (CSMA) to solve the four problems mentioned above. Our approach can deal with the problem of missing values and outliers via SVD-L1. The Random Projection method is used to obtain the fast low-rank approximation of a given multifactor dataset. In addition, it is able to preserve the geometry of the original data. Our CSMA method can be used efficiently for multiple purposes, e.g. noise and outlier removal, estimation of missing values, biometric applications. We show that CSMA method can achieve good results and is very efficient in the inpainting problem as compared to [1], [2]. Our method also achieves higher face recognition rates compared to LRTC, SPMA, MPCA and some other methods, i.e. PCA, LDA and LPP, on three challenging face databases, i.e. CMU-MPIE, CMU-PIE and Extended YALE-B.

Modeling the face aging process is a challenging task due to large and non-linear variations present in different stages of face development. This paper presents a deep model approach for face age progression that can efficiently capture the non-linear aging process and automatically synthesize a series of age-progressed faces in various age ranges. In this approach, we first decompose the long-term age progress into a sequence of short-term changes and model it as a face sequence. The Temporal Deep Restricted Boltzmann Machines based age progression model together with the prototype faces are then constructed to learn the aging transformation between faces in the sequence. In addition, to enhance the wrinkles of faces in the later age ranges, the wrinkle models are further constructed using Restricted Boltzmann Machines to capture their variations in different facial regions. The geometry constraints are also taken into account in the last step for more consistent age-progressed results. The proposed approach is evaluated using various face aging databases, i.e. FGNET, Cross-Age Celebrity Dataset (CACD) and MORPH, and our collected large-scale aging database named AginG Faces in the Wild (AGFW). In addition, when ground-truth age is not available for input image, our proposed system is able to automatically estimate the age of the input face before aging process is employed.

This paper presents a novel Robust Deep Appearance Models (RDAMs) approach to learn the non-linear correlation between shape and texture of face images. In this approach, two crucial components of face images, i.e. shape and texture, are represented by Deep Boltzmann Machines and Robust Deep Boltzmann Machines (RDBM), respectively. The RDBM, an alternative form of Robust Boltzmann Machines, can separate corrupted/occluded pixels in the texture modeling to achieve better reconstruction results. The two models are connected by Restricted Boltzmann Machines at the top layer to jointly learn and capture the variations of both facial shapes and appearances. This paper also introduces new fitting algorithms with occlusion awareness through the mask obtained from the RDBM reconstruction. The proposed approach is evaluated in various applications by using challenging face datasets, i.e. Labeled Face Parts in the Wild (LFPW), Helen, EURECOM and AR databases, to demonstrate its robustness and capabilities.

In this paper, we propose two new approaches using the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) for tracking 3D hand poses. The first approach is a detection based algorithm while the second is a data driven method. Our first contribution is a new tracking-by-detection strategy extending the CNN based single frame detection method to a multiple frame tracking approach by taking into account prediction history using RNN. Our second contribution is the use of RNN to simulate the fitting of a 3D model to the input data. It helps to relax the need of a carefully designed fitting function and optimization algorithm. With such strategies, we show that our tracking frameworks can automatically correct the fail detection made in previous frames due to occlusions. Our proposed method is evaluated on two public hand datasets, i.e. NYU and ICVL, and compared against other recent hand tracking methods. Experimental results show that our approaches achieve the state-of-the-art accuracy and efficiency in the challenging problem of 3D hand pose estimation.

Summary Support vector machine (SVM) is one of the most popular classification techniques in pattern recognition community. However, because of outliers in the training samples, SVM tends to perform poorly under such circumstances. In this paper, we borrow the idea from compressive sensing by introducing an extra term to the objective function of the standard SVM in order to achieve a sparse representation. Furthermore, instead of using thel0norm, we adopt thel1norm in our sparse SVM. In most cases, our method achieves higher classification rates than the standard SVM because of sparser support vectors and is more robust to outliers in the datasets. Experimental results show that our proposed SVM is efficient in pattern recognition applications. Copyright © 2015 John Wiley & Sons, Ltd.

The “interpretation through synthesis”, i.e. Active Appearance Models (AAMs) method, has received considerable attention over the past decades. It aims at “explaining” face images by synthesizing them via a parameterized model of appearance. It is quite challenging due to appearance variations of human face images, e.g. facial poses, occlusions, lighting, low resolution, etc. Since these variations are mostly non-linear, it is impossible to represent them in a linear model, such as Principal Component Analysis (PCA). This paper presents a novel Deep Appearance Models (DAMs) approach, an efficient replacement for AAMs, to accurately capture both shape and texture of face images under large variations. In this approach, three crucial components represented in hierarchical layers are modeled using the Deep Boltzmann Machines (DBM) to robustly capture the variations of facial shapes and appearances. DAMs are therefore superior to AAMs in inferring a representation for new face images under various challenging conditions. In addition, DAMs have ability to generate a compact set of parameters in higher level representation that can be used for classification, e.g. face recognition and facial age estimation. The proposed approach is evaluated in facial image reconstruction, facial super-resolution on two databases, i.e. LFPW and Helen. It is also evaluated on FG-NET database for the problem of age estimation.

The use of Higher-Order Singular Value Decomposition (HOSVD) and other tensor decomposition methods are popular in the face recognition domain, yet a direct application to handwritten character recognition has not shown promising results so far. Character recognition is commonly performed in two steps: feature extraction and classification. In this paper, we propose a feature extraction algorithm based on HOSVD which is then combined with standard statistical classification. The algorithm constructs a tensor from the training data and applies HOSVD in order to obtain a feature extractor matrix for arbitrary character images. We evaluate the proposed handwriting features in combination with SVM classification for character recognition on the CEDAR benchmark data set. The results indicate that our proposed approach significantly outperforms the standard HOSVD classification method.

Recently the theories of sparse representation (SR) and dictionary learning (DL) have brought much attention and become powerful tools for pattern recognition and computer vision. Due to the fact that images can be represented in a sparse and compressible way with respect to some dictionaries, these theories have shown successful applications in many different areas including face recognition, image denoising and in painting, medical imaging, image classification and registration, motion estimation, and many more. Over a relatively short time, many improvements and innovative ideas using SR and DL have been developed. However, very little published work is found in the application of these theories on handwritten character recognition. One question comes to mind is whether these theories could produce good results for handwritten character recognition as in the case of other applications. In this paper, we would like to address this question by investigating various applications of the theories to handwritten character recognition. Experiments were conducted in both handwritten digits and alphabetical characters on three benchmark databases: MNIST, USPS, and CEDAR. The results showed that while this approach can achieve good results, it cannot beat the state of the art. The main advantage of this approach is that it does not require the choice of features and hence it may reduce computational cost.

Face recognition under various conditions such as illumination, poses, expression, and occlusion has been one of the most challenging problems in computer vision. Over the last few years there has been significant attention paid to the low-rank approximation (LRA) and sparse representation (SR) techniques. The applications of these techniques have appeared in many different areas ranging from handwritten character recognition to multi-factor face recognition. In this paper, we will review some of the most recent works using LRA and SR in the multi-factor face recognition problem, and present a novel framework to improve their performance in the recognition of faces under various affecting conditions. Our results are comparable to or better than the state-of-the-art in this area.

In this letter, we study the Ramanujan Sums (RS) transform by means of matrix multiplication. The RS are orthogonal in nature and therefore offer excellent energy conservation capability. The 1-D and 2-D forward RS transforms are easy to calculate, but their inverse transforms are not defined in the literature for non-even function$ ({\rm mod}~ {\rm M}) $. We solved this problem by using matrix multiplication in this letter.

We present a statistical hypothesis testing method for handwritten word segmentation algorithms. Our proposed method can be used along with any word segmentation algorithm in order to detect over-segmented or under-segmented errors or to adapt the word segmentation algorithm to new data in an unsupervised manner. The main idea behind the proposed approach is to learn the geometrical distribution of words within a sentence using a Markov chain or a Hidden Markov Model (HMM). In the former, we assume all the necessary information is observable, where in the latter, we assume the minimum observable variables are the bounding boxes of the words, and the hidden variables are the part of speech information. Our experimental results on a benchmark database show that not only we can achieve a lower over-segmentation and under-segmentation error rate, but also a higher correct segmentation rate as a result of the proposed hypothesis testing.

This paper introduces an advanced age-determination technique using hybrid facial features and Kernel Spectral Regression, a nonlinear dimensionality reduction method. In the preprocessing stage, the logarithmic nonsubsampled contourlet transform (NSCT) is conducted to denoise and amplify facial wrinkles that help to distinguish young faces from elder ones. Then the hybrid facial features that combine both local and holistic features are extracted from the preprocessed images. Our novel Uniform Local Ternary Patterns (ULTP) are used as the local features. Meanwhile the holistic features are extracted by using the Active Appearance Model (AAM) to encode each face. Kernel Spectral Regression is used to minimize inter-class distances while maximizing intra-class distances of feature sets. These reduced features are used to classify faces into two age groups (age-classification). An age-determination function is then constructed for each age group in accordance with physiological growth periods for humans - pre-adult (youth) and adult. Compared to published results, this method yields promising results in overall mean absolute error (MAE), mean absolute error per decade of life (MAE/D), and cumulative match score in various face aging corpuses.

In this paper, we will present a novel framework of utilizing periocular region for age invariant face recognition. To obtain age invariant features, we first perform preprocessing schemes, such as pose correction, illumination and periocular region normalization. And then we apply robust Walsh-Hadamard transform encoded local binary patterns (WLBP) on preprocessed periocular region only. We find the WLBP feature on periocular region maintains consistency of the same individual across ages. Finally, we use unsupervised discriminant projection (UDP) to build subspaces on WLBP featured periocular images and gain 100% rank-1 identification rate and 98% verification rate at 0.1% false accept rate on the entire FG-NET database. Compared to published results, our proposed approach yields the best recognition and identification results.

In this paper we propose a novel Contourlet Appearance Model (CAM) that is more accurate and faster at localizing facial landmarks than Active Appearance Models (AAMs). Our CAM also has the ability to not only extract holistic texture information, as AAMs do, but can also extract local texture information using the Nonsubsampled Contourlet Transform (NSCT). We demonstrate the efficiency of our method by applying it to the problem of facial age estimation. Compared to previously published age estimation techniques, our approach yields more accurate results when tested on various face aging databases.

A vast number of historical and badly degraded document images can be found in libraries, public, and national archives. Due to the complex nature of different artifacts, such poor quality documents are hard to read and to process. In this paper, a novel adaptive binarization algorithm using ternary entropy-based approach is proposed. Given an input image, the contrast of intensity is first estimated by a grayscale morphological closing operator. A double-threshold is generated by our Shannon entropy-based ternarizing method to classify pixels into text, near-text, and non-text regions. The pixels in the second region are relabeled by the local mean and the standard deviation. Our proposed method classifies noise into two categories which are processed by binary morphological operators, shrink and swell filters, and graph searching strategy. The method is tested with three databases that have been used in the Document Image Binarization Contest 2009 (DIBCO 2009), the Handwriting Document Image Binarization Contest 2010 (H-DBCIO 2010), and the International Conference on Frontier in Handwriting Recognition 2010 (ICFHR 2010). The evaluation is based upon nine distinct measures. Experimental results show that our proposed algorithm outperforms other state-of-the-art methods.

This paper presents a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain such as JPEG 2000. The proposed approach is capable of improving both global and local contrast as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in the different scales. Experimental results show that the proposed method can enhance wavelet-coded image computationally efficiently with high image quality and less noise or other artifact.

The denoising of a natural signal/image corrupted by Gaussian white noise is a classical problem in signal/image processing. However, it is still in its infancy to denoise high dimensional data. In this paper, we extended Sendur and Selesnick's bivariate wavelet thresholding from two-dimensional (2D) image denoising to three-dimensional (3D) data cube denoising. Our study shows that bivariate wavelet thresholding is still valid for 3D data cubes. Experimental results show that bivariate wavelet thresholding on 3D data cube is better than performing 2D bivariate wavelet thresholding on every spectral band separately, VisuShrink, and Chen and Zhu's 3-scale denoising.

This paper presents an advanced age-determination technique that combines holistic and local features derived from an image of the face. A 30×1 Active Appearance Model (AAM) linear encoding of each face is produced to work as holistic features. Meanwhile, local features are extracted by using Local Ternary Patterns (LTP). These combined features are used to classify faces into one of two age groups (age-classification). An age-determination function is then constructed for each age group in accordance with physiological growth periods for humans - pre-adult (youth) and adult. Compared to published results, this method yields the highest accuracy rates in overall mean absolute error (MAE), mean absolute error per decade of life (MAE/D), and cumulative match score.

Automatic retinal image segmentation is desirable for some disease diagnosis such as diabetes. In this paper, we propose a new image segmentation method to segment retinal images. The new method is based on the Mumford-Shah (MS) model. As a region-based approach, the MS model is a good segmentation technique. However, due to non-uniform illumination, some traditional approximations of the MS model cannot deal with this type of problems. We present a new method that requires no approximations. Instead, Gabor wavelet filter is used, and the method can segment objects with complicated image intensity distribution. The method is used to detect blood vessels in retinal images. The results are comparable with or better than state-of-the-art. Our method requires no training and is relatively fast.

A novel and efficient method for correction of slant angles in handwritten numeral strings is proposed. For the first time, the statistical distribution of slant angles in handwritten numerals is investigated and the effects of slant correction on the segmentation of handwritten numeral strings are shown. In our proposed slant correction method, utilizing geometric features, a Component Slant Angle (CSA) is estimated for each connected component independently. A weighted average is then used to compute the String Slant Angle (SSA), which is applied uniformly to correct the slant of all the components in numeral strings. Our experimental results have revealed novel statistics for slant angles of handwritten numeral strings, and also showed that slant correction can significantly improve extraction of segmentation features and segmentation accuracy of touching numerals. Comparison between our slant correction algorithm and similar algorithms in the literature show that our algorithm is more efficient, and on average it has a faster running time.

A new isolated handwritten Farsi numeral recognition algorithm is proposed in this paper, which exploits the sparse and over-complete structure from the handwritten Farsi numeral data. In this research, the sparse structure is represented as an over-complete dictionary, which is learned by the K-SVD algorithm. These atoms in this dictionary are adopted to initialize the first layer of the convolutional neural network (CNN), the latter is then trained to do the classification task. Data distortion techniques are also applied to promote the generalization capability of the trained classifier. Experiments have shown that good results have been achieved in CENPARMI handwritten Farsi numeral database.

Image inpainting or completion is a technique to restore a damaged image. Recently various approaches have been proposed. Wavelet transform has been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics. We propose to utilize the advantages of wavelet transforms for image inpainting. Unlike other inpainting algorithms, we can expect better global structure estimation of a damaged region in addition to shape and texture properties.

A sparse representation based method is proposed for text detection from scene images. We start with edge information extracted using Canny operator and then group these edge points into connected components. Each connected component is labeled as text or non-text by a two-level labeling process: pixel level labeling and connected component labeling. The core of the labeling process is a sparsity test using an over-complete dictionary, which is learned from edge segments of isolated character images. Layout analysis is further applied to verify these text candidates. Experimental results show that improvements in both recall rate and detection accuracy in text detection have been achieved.

As a region-based approach, the Mumford-Shah (MS) model is a robust image segmentation technique. However, the solution of the MS model is not trivial. Although some alternative approaches have been presented, these methods are either inefficient or applicable only to some special cases. We present a new model which consists of two terms, the length of the segmentation curve and the high-frequency component in the regions. Because only one variable needs to be solved, the method of solution is very efficient. Using the level set method, the approach can segment objects with complicated image intensity distribution without any approximations. In addition, the new model can segment both step and roof edges.

A novel text segmentation method from complex background is presented in this paper. The idea is inspired by the recent development in searching for the sparse signal representation among a family of over-complete atoms, which is called a dictionary. We assume that the image under investigation is composed of two components: the foreground text and the complex background. We further assume that the latter can be modeled as a piece-wise smooth function. Then we choose two dictionaries, where the first one gives sparse representation to one component and non-sparse representation to another while the second one does the opposite. By looking for the sparse representations in each dictionary, we can decompose the image into the two composing components. After that, text segmentation can be easily achieved by applying simple thresholding to the text component. Preliminary experiments show some promising results.

A new palmprint classification method is proposed in this paper by using the dual-tree complex wavelet transform. The dual-tree complex wavelet transform has such important properties as the approximate shift-invariance and high directional selectivity. These properties are very important in invariant palmprint classification. Support vector machines are used as a classifier and the Gaussian radial basis function kernel is selected in the experiments. Experimental results show that the dual-tree complex wavelet features outperform the scalar wavelet features, and three previously developed methods. We conclude that the dual-tree complex wavelet features should be used for invariant palmprint classification instead of the scalar wavelet features.

In this paper, we derive the general estimation rule in the wavelet domain to obtain the denoised coefficients from the noisy image based on the multivariate statistical theory. We define a parametric multivariate generalized Gaussian distribution (MGGD) model which closely fits the actual distribution of wavelet coefficients in clean natural images. The multivariate model makes it possible to exploit the dependency between the estimated wavelet coefficients and their neighbours or other coefficients in different subbands. Also it can be shown that some of the existing methods based on statistical modeling are subsets of our multivariate approach. Our method could achieve high quality image denoising. Among the comparable image denoising methods using the same type of wavelet (esp. Daubechies 8) filter, our results produce comparatively higher peak signal to noise ratio (PSNR).

Multi-channel Gabor filtering has been widely used in texture classification. In this paper, Gabor filters have been applied to the problem of script identification in printed documents. Our work is divided into two stages. Firstly, a Gabor filter bank is appropriately designed so that extracted rotation-invariant features can handle scripts that are similar in shape and even share many characters. Secondly, the steerability property of Gabor filters is exploited to reduce the high computation cost resulted from the frequent image filtering, which is a common problem encountered in Gabor filter related applications. Results from preliminary experiments are quite promising, where Chinese, Japanese, Korean and English are considered. Over 98.5 % language identification rate can be achieved while image filtering operations have been reduced by 40%.

The recognition of handwritten numerals is a challenging task in pattern recognition. It can be considered as one of the benchmarks in evaluating feature extraction methods and the performance of classifiers. In this paper, we propose a new method to improve the recognition accuracy of handwritten numerals by using hybrid feature extraction and random feature selection. First, we present seven feature extraction methods. A novel multi-class divergence criterion for large scale feature analysis is proposed and a random feature selection strategy is used to congregate three new hybrid feature sets. The new congregated features are complementary as they are formed from different original feature sets extracted by different means. Experiments conducted on MNIST database show that our proposed method can increase the recognition accuracy.

In this paper we have generalized the Mumford-Shah (MS) model to detect roof edges. It is found that many previous models cannot detect edges with low contrast. We have studied a variety of different models of energy minimization a la Mumford-Shah approach for image segmentation. The model proposed in this paper is better than the classical piecewise constant approximation since it can detect the low contrast edges of objects. The validity of the new model is demonstrated by experimental results.

Recently, Chan and Vese developed an active contour model for image segmentation and smoothing by using piecewise constant and smooth representation of an image. Tsai et al. also independently developed a segmentation and smoothing method similar to the Chan and Vese piecewise smooth approach. These models are active contours based on the Mumford-Shah variational approach and the level-set method. In this paper, we develop a new hierarchical method which has many advantages compared to the Chan and Vese multiphase active contour models. First, unlike previous works, the curve evolution partial differential equations (PDEs) for different level-set functions are decoupled. Each curve evolution PDE is the equation of motion of just one level-set function, and different level-set equations of motion are solved in a hierarchy. This decoupling of the motion equations of the level-set functions speeds up the segmentation process significantly. Second, because of the coupling of the curve evolution equations associated with different level-set functions, the initialization of the level sets in Chan and Vese's method is difficult to handle. In fact, different initial conditions may produce completely different results. The hierarchical method proposed in this paper can avoid the problem due to the choice of initial conditions. Third, in this paper, we use the diffusion equation for denoising. This method, therefore, can deal with very noisy images. In general, our method is fast, flexible, not sensitive to the choice of initial conditions, and produces very good results.

In this paper, we propose a mobile terminal (MT) location registration/update model. In this model, the registration decision is based on two factors-the time elapsed since last call arrival and the distance the MT has traveled since last registration. It is established that the optimal registration strategy can be represented by a curve. Only when the state of the system reaches this curve is a registration performed. In order for an MT to calculate its traveled distance, an interactive implementation scheme and a distance calculation algorithm are developed. When the call interarrival times are independent and geometrically distributed, the proposed model becomes a distance-based model and, in this case, the optimal registration strategy is of threshold structure. For the distance-based model, a single sample path-based ordinal optimization algorithm is devised. In this algorithm, without any knowledge about the system parameters, the MT observes the system state transitions, estimates the ordinal of a set of strategies, and updates the registration strategy adaptively. Since only a single sample path is used, this algorithm can be implemented online. Several numerical examples are provided to compare the proposed model and the existing ones.

The denoising of a natural image corrupted by Gaussian noise is a classical problem in signal or image processing. Donoho and his coworkers at Stanford pioneered a wavelet denoising scheme by thresholding the wavelet coefficients arising from the standard discrete wavelet transform. This work has been widely used in science and engineering applications. However, this denoising scheme tends to kill too many wavelet coefficients that might contain useful image information. In this paper, we propose one wavelet image thresholding scheme by incorporating neighbouring coefficients, namely NeighShrink. This approach is valid because a large wavelet coefficient will probably have large wavelet coefficients as its neighbours. Experimental results show that NeighShrink is better than the Wiener filter and the conventional wavelet denoising approaches: VisuShrink and SUREShrink. We also investigate different neighbourhood sizes and find that a size of 3/spl times/3 is the best among all window sizes.

Multiwavelets give better results than single wavelets for signal denoising. We study multiwavelet thresholding by incorporating neighboring coefficients. Experimental results show that this approach is better than the conventional approach, which only uses the term-by-term multiwavelet denoising. Also, it outperforms neighbor single wavelet denoising for some standard test signals and real-life images. This is an extension to Cai and Silverman's (see Sankhya: Ind. J. Stat. B, pt.2, vol.63, p.127-148, 2001) work.

Invariance and low dimension of features are of crucial significance in pattern recognition. This paper proposes a novel orthonormal shell Fourier descriptor that satisfies all of these demands. This method first performs orthonormal shell decomposition on the line moment that is obtained from the 2-D pattern, then applies Fourier transform on each scale of the shell coefficients. Unlike other existing wavelet-based methods, our method allows applying common orthonormal wavelets, such as Daubechies, Symmlet and Coiflet, therefore it is simple to implement. We study the structure of the filter used and develop a fast algorithm to rapidly compute the spectra of orthonormal shell coefficients. The complexity of the proposed descriptor is O(n log n). We apply a coarse-to-fine strategy to search the image database; the matching is very quick because of the multiscale feature structure. The effectiveness of this new descriptor is demonstrated by a series of experiments as well as the comparison with other descriptors. The proposed descriptor is robust to white noise.

This paper proposes a novel method called Wavelet-Sparse-Matrix (WSM) to extract the spatial features of 2-D objects for classifying objects that have subtle differences. The differences between these objects are present in the spatial orientations of the objects, or in the local positions of points on the contours of the objects. The separable wavelets are able to distinguish these differences and to separate them into three sparse subpatterns. Sparse matrix technique has the ability to rearrange nonzero elements in a sparse matrix by moving them as close together as possible. WSM method is a combination of these two techniques which can considerably improve the distinction of slightly dissimilar objects. Experiments are conducted, which include a series of discriminative simulations and comparisons with Fourier descriptor and Zernike moment invariant. These experiments verify the feasibility and effectiveness of the WSM method.

Feature extraction and pattern classification are two key components in a pattern recognition system. In our approach, each image is represented by a 2D Fourier descriptor which is translation-, rotation-, and scale-invariant. We define a new metric, named the Hellinger-Kakutani metric for measuring the distance between two Fourier descriptors for classification. This metric is filtration-invariant, hence can be used on noisy images. The method is applied to a set of 22 Chinese characters, which contains 7 subsets of similar characters. The rate of accurate recognition is then reported.

This correspondence presents a segmentation and fitting method using a new robust estimation technique. We present a robust estimation method with high breakdown point which can tolerate more than 80% of outliers. The method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type. From K samples, we choose one set of sample points that determines a best-fit equation for the largest homogeneous surface patch in the region. This choice is made by measuring a residual consensus (RESC), using a compressed histogram method which is effective at various noise levels. After we get the best-fit surface parameters, the surface patch can be segmented from the region and the process is repeated until no pixel left. The method segments the range image into planar and quadratic surfaces. The RESC method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus. A genetic algorithm is also incorporated to accelerate the random search.>

The authors randomly sample appropriate range image points and solve equations determined by these points for the parameters of selected primitive type. From K samples they measure residual consensus to choose one set of sample points that determines an equation having the best fit for the largest homogeneous surface patch in the current processing region. The residual consensus is measured by a compressed histogram method that works at various noise levels. The estimated surface patch is extracted out of the processing region to avoid further computation. A genetic algorithm is used to accelerate the search speed.>

An optimal pairing scheme in associative memory classifier is discussed, especially when Hadamard vectors are selected as inner codes. As such a scheme is applied to recognize a set of multi-font Chinese characters, an improvement in the classification performance of this associative memory network is observed.>

The splitting-integrating method is a technique developed for the normalization of images by inverse transformation. It does not require solving nonlinear algebraic equations and is much simpler than any existing algorithm for the inverse nonlinear transformation. Moreover, its solutions have a high order of convergence, and the images obtained through T/sup -1/ are free from superfluous holes and blanks, which often occur in transforming digitized images by other approaches. Application of the splitting-integrating method can be extended to supersampling in computer graphics, such as picture transformations by antialiasing, inverse nonlinear mapping, etc.>

A harmonic model of shape transformations is presented. In this model, harmonic functions are governed by the Laplace equation. This model can convert all image or a pattern to another with arbitrary shapes. The transformation process is harmonic, without abruptness and discontinuity. This model can be used to generate and recognize handwritten Roman letters and Chinese characters, fingerprints, and other types of digitized images and patterns. The algorithms of the harmonic models involve partial differential equations and their numerical solutions. Therefore, an intrinsic link between pattern images and numerical methods is presented.>

This paper presents linear and bilinear shape transformations including basic transformations, analyzes their geometric properties, and provides computer algorithms. The shape transformations can be used to simplify the recognition of Roman letters, Chinese characters and other pictorial patterns by normalizing their shapes to the standard forms. Important theoretical analyses have been performed to illustrate that the linear and bilinear transformations are applicable to computer recognition of digitized patterns. A number of pictorial examples have been computed to confirm the analyses and conclusions made.

New splitting-shooting methods are presented for nonlinear transformations T: ( xi , eta ) to (x,y) where x=x( xi , eta ), y=y( xi , eta ). These transformations are important in computer vision, image processing, pattern recognition, and shape transformations in computer graphics. The methods can eliminate superfluous holes or blanks, leading to better images while requiring only modest computer storage and CPU time. The implementation of the proposed algorithms is simple and straightforward. Moreover, these methods can be extended to images with gray levels, to color images, and to three dimensions. They can also be implemented on parallel computers or VLSI circuits. A theoretical analysis proving the convergence of the algorithms and providing error bounds for the resulting images is presented. The complexity of the algorithms is linear. Graphical and numerical experiments are presented to verify the analytical results and to demonstrate the effectiveness of the methods.>

Four nonlinear shape models are presented: polynomial, Coons, perspective, and projective modes. Algorithms and some properties of these models are provided. For a given physical model, such as a perspective model, comparisons are made with other mathematical models. It is proved that, under certain conditions, the perspective models can be replaced by the Coons models. Problems related to substitution and approximation of practical models that facilitate digital image processing are raised and discussed. Experimental results on digital images are presented.>

In 1979, G. K. Manacher showed that the Ford-Johnson sorting algorithm [FJA], acting on t real numbers, can be beaten for an infinite set of values t . These values form a partial cover of constant density not close to 1 over an initial sequence of each band running from u k = ⌊(4/3)2 k ⌋ to u k +l - 1. This early result depended on showing that the Hwang-Lin merging algorithm [HLA], merging m elements with n , m ≠ n , could be surpassed by cm comparisons, where c is an arbitrary small positive constant. In this paper, it is shown that the FJA can be beaten for a set of integers of asymptotic density 1 under the greatly weakened assumption that the HLA can be surpassed by only (1/2 + ϵ)log m comparisons, with ϵ a small positive constant. The even weaker assumption that no improvement in the HLA exists, but that an isolated value t o exists for which the FJA can be surpassed by only (1 + ϵ)log t o comparisons yields the same result. Only for a set of “refractory” integers of size about t 1/2 in the neighborhood of each u k does the FJA fail to be beaten. All these results depend on a new technique for obtaining optimum sort-merge sequences for best-possible sorting given a merging method. The technique turns out to be amenable to precise asymptotic analysis. When the technique is applied using the most powerful known merging algorithm [Christen's], the density mentioned above is still 1, but islands of refractory points still remain, this time forming sets provably of size Θ(log 2 t ) in the neighborhood of each u k . It is shown that if “information theoretic” merging were achievable, the FJA could be beaten for all t > u 10 = 1365. From these results and a few others, we adduce evidence in support of our main conjecture: that even optimum combinations of optimum merging and Ford-Johnson sorting will not beat the FJA when t = u k , but will instead produce refractory regions of size Θ(log 2 t ) in the neighborhood of each λ .

Solving flame propagation problems with the method of lines leads to large systems of ordinary differential equations. These systems are usually solved by Backward Differentiation Formula (BDF) methods, such as by LSODE of Hindmarsh. Recently, Rosenbrock methods turned out to be rather successful for integrating small systems with inexpensive function and Jacobian evaluations. However, no test has been done on the performance of some recently developed Rosenbrock codes in a situation in which the dimension of the system is large, for example, over one hundred equations. These Rosenbrock codes performed quite well on the STIFF DETEST and other small systems. The aim of this paper is to investigate the performance of the Rosenbrock methods in solving the flame propagation problem by the method of lines.

Some A-stable and L-stable Rosenbrock type (semi-implicit Runge-Kutta) methods accurate to the fourth local order with only one computation of a Jacobian matrix per step of mtegratJon are constructed for the solution of the Cauchy problem for systems of stiff ordinary differential equations Numerical experiments show high efficiency of the proposed methods for excessively stiff systems

No abstract available.