Directional multiscale modeling of images using the contourlet transform

Adaptive Contourlet Fusion Clustering for SAR Image Change Detection

In this paper, a novel unsupervised change detection method called adaptive Contourlet fusion clustering based on adaptive Contourlet fusion and fast non-local clustering is proposed for multi-temporal synthetic aperture radar (SAR) images. A binary image indicating changed regions is generated by a novel fuzzy clustering algorithm from a Contourlet fused difference image. Contourlet fusion uses complementary information from different types of difference images. For unchanged regions, the details should be restrained while highlighted for changed regions. Different fusion rules are designed for low frequency band and high frequency directional bands of Contourlet coefficients. Then a fast non-local clustering algorithm (FNLC) is proposed to classify the fused image to generate changed and unchanged regions. In order to reduce the impact of noise while preserve details of changed regions, not only local but also non-local information are incorporated into the FNLC in a fuzzy way. Experiments on both small and large scale datasets demonstrate the state-of-the-art performance of the proposed method in real applications.

A combined HMM-PCNN model in the contourlet domain for image data compression

Multiscale geometric analysis (MGA) is not only characterized by multi-resolution, time-frequency localization, multidirectionality and anisotropy, but also outdoes the limitations of wavelet transform in representing high-dimensional singular data such as edges and contours. Therefore, researchers have been exploring new MGA-based image compression standards rather than the JPEG2000 standard. However, due to the difference in terms of the data structure, redundancy and decorrelation between wavelet and MGA, as well as the complexity of the coding scheme, so far, no definitive researches have been reported on the MGA-based image coding schemes. In addressing this problem, this paper proposes an image data compression approach using the hidden Markov model (HMM)/pulse-coupled neural network (PCNN) model in the contourlet domain. First, a sparse decomposition of an image was performed using a contourlet transform to obtain the coefficients that show the multiscale and multidirectional characteristics. An HMM was then adopted to establish links between coefficients in neighboring subbands of different levels and directions. An Expectation-Maximization (EM) algorithm was also adopted in training the HMM in order to estimate the state probability matrix, which maintains the same structure of the contourlet decomposition coefficients. In addition, each state probability can be classified by the PCNN based on the state probability distribution. Experimental results show that the HMM/PCNN -contourlet model proposed in this paper leads to better compression performance and offer a more flexible encoding scheme.

Thermal and Visual Imaging to Assist with Juvenile Idiopathic Arthritis Examination of the Knees

Juvenile idiopathic arthritis (JIA) causes inflammation of the joints, and it is frequently associated with their pain and stiffness. Its timely diagnosis is important to avoid its progressive damage to the bones and cartilage. Increases in the joint’s temperature and redness could be indicators of active JIA, hence their accurate quantification could assist with diagnosis. Thermal and visual images of the knees in 20 JIA participants (age: mean = 11.2 years, standard deviation = 2.3 years) were studied. The median temperature of knees with active inflammation was 3.198% higher than that of inactive knees. This difference, examined by a Wilcoxon signed-rank test, was statistically significant (p = 0.0078). In six out of the eight participants who had one active inflamed knee, thermal imaging identified the corresponding knee as warmer. In 16 out of 20 participants, the knee identified as warmer by thermal imaging was also identified as having a greater colour change by visual imaging as compared to their respective reference regions. The devised methods could accurately quantify the colour and temperature of the knees. It was concluded that thermal and visual imaging methods can be valuable in examining JIA. Further studies involving a larger number of participants and more detailed explorations would be needed prior to clinical application.

Feature Extraction with Discrete Non-Separable Shearlet Transform and Its Application to Surface Inspection of Continuous Casting Slabs

A new feature extraction technique called DNST-GLCM-KSR (discrete non-separable shearlet transform-gray-level co-occurrence matrix-kernel spectral regression) is presented according to the direction and texture information of surface defects of continuous casting slabs with complex backgrounds. The discrete non-separable shearlet transform (DNST) is a new multi-scale geometric analysis method that provides excellent localization properties and directional selectivity. The gray-level co-occurrence matrix (GLCM) is a texture feature extraction technology. We combine DNST features with GLCM features to characterize defects of the continuous casting slabs. Since the combination feature is high-dimensional and redundant, kernel spectral regression (KSR) algorithm was used to remove redundancy. The low-dimension features obtained and labels data were inputted to a support vector machine (SVM) for classification. The samples collected from the continuous casting slab industrial production line—including cracks, scales, lighting variation, and slag marks—and the proposed scheme were tested. The test results show that the scheme can improve the classification accuracy to 96.37%, which provides a new approach for surface defect recognition of continuous casting slabs.

Detecting the Media-adventitia Border in Intravascular Ultrasound Images through a Classification-based Approach

The detection of the media-adventitia (MA) border in intravascular ultrasound (IVUS) images is essential for vessel assessment and disease diagnosis. However, it remains a challenging task, considering the existence of plaque, calcification, and various artifacts. In this article, an effective method based on classification is proposed to extract the MA border in IVUS images. First, a novel morphologic feature describing the relative position of each structure relative to the MA border, called RPES for short, is proposed. Then, the RPES feature and other features are employed in a multiclass extreme learning machine (ELM) to classify IVUS images into nine classes including the MA border and other structures. At last, a modified snake model is employed to effectively detect the MA border in the rectangular domain, in which a modified external force field is constructed on the basis of local border appearances and classification results. The proposed method is evaluated on a public dataset with 77 IVUS images by three indicators in eight situations, such as calcification and a guide wire artifact. With the proposed RPES feature, detection performances are improved by more than 39 percent, which shows an apparent advantage in comparative experiments. Furthermore, compared with two other existing methods used on the same dataset, the proposed method achieves 18 of the best indicators among 24, demonstrating its higher capability in detecting the MA border.

Fractional-order Darwinian PSO-based feature selection for media-adventitia border detection in intravascular ultrasound images

Media-adventitia (MA) border delineates the outer appearance of arterial wall in intravascular ultrasound (IVUS) image. The detection of MA border is a challenging topic due to many difficulties such as complicated intravascular structures, intrinsic artifacts and image noises. We propose a classification-based MA border detection method with an embedded feature selection technique. The feature selection technique is based on Fractional-order Darwinian particle swarm optimization (FODPSO) algorithm. By employing feature selection, 293-dimension features including multi-scale features, gray-scale features and morphological feature are reducing to 37-dimension. The border detection method with feature selection is tested on a public dataset extracted from in-vivo pullbacks of human coronary arteries, which contains 77 IVUS images. Three indicators, Jaccard (JACC), Hausdorff Distance (HD) and Percentage of Area Difference (PAD), are measured for quantitative evaluation. Detection with 293-dimension features obtains JACC 0.79, HD 1.41 and PAD 0.16, while detection with 37-dimension features obtains JACC 0.83, HD 1.27 and PAD 0.12, indicating that the FODPSO-based feature selection method improves MA border detection by JACC 0.04, HD 0.14 and PAD 0.04. Furthermore, the proposed border detection method acquires better performances compared with two other automatic methods conducted on the same dataset available in literature.

Enhancing vascular visualization in laser speckle contrast imaging of blood flow using multi-focus image fusion

Laser speckle contrast imaging (LSCI) is a full-field optical imaging method for monitoring blood flow and vascular morphology with high spatiotemporal resolution. However, due to the limited depth of field of optical system, it is difficult to capture a clear blood flow image with all blood vessels focused, especially for the non-planar biological tissues. In this study, a multi-focus image fusion method based on contourlet transform is introduced to reduce the misfocus effects in LSCI. The experimental results suggest that this method can provide an all-in-focus blood flow image, which is convenient to observe the blood vessels.

Automated detection and classification of liver fibrosis stages using contourlet transform and nonlinear features

BACKGROUND AND OBJECTIVE

Liver fibrosis is a type of chronic liver injury that is characterized by an excessive deposition of extracellular matrix protein. Early detection of liver fibrosis may prevent further growth toward liver cirrhosis and hepatocellular carcinoma. In the past, the only method to assess liver fibrosis was through biopsy, but this examination is invasive, expensive, prone to sampling errors, and may cause complications such as bleeding. Ultrasound-based elastography is a promising tool to measure tissue elasticity in real time; however, this technology requires an upgrade of the ultrasound system and software. In this study, a novel computer-aided diagnosis tool is proposed to automatically detect and classify the various stages of liver fibrosis based upon conventional B-mode ultrasound images.

METHODS

The proposed method uses a 2D contourlet transform and a set of texture features that are efficiently extracted from the transformed image. Then, the combination of a kernel discriminant analysis (KDA)-based feature reduction technique and analysis of variance (ANOVA)-based feature ranking technique was used, and the images were then classified into various stages of liver fibrosis.

RESULTS

Our 2D contourlet transform and texture feature analysis approach achieved a 91.46% accuracy using only four features input to the probabilistic neural network classifier, to classify the five stages of liver fibrosis. It also achieved a 92.16% sensitivity and 88.92% specificity for the same model. The evaluation was done on a database of 762 ultrasound images belonging to five different stages of liver fibrosis.

CONCLUSIONS

The findings suggest that the proposed method can be useful to automatically detect and classify liver fibrosis, which would greatly assist clinicians in making an accurate diagnosis.

Sharpness-Aware Low-Dose CT Denoising Using Conditional Generative Adversarial Network

Low-dose computed tomography (LDCT) has offered tremendous benefits in radiation-restricted applications, but the quantum noise as resulted by the insufficient number of photons could potentially harm the diagnostic performance. Current image-based denoising methods tend to produce a blur effect on the final reconstructed results especially in high noise levels. In this paper, a deep learning-based approach was proposed to mitigate this problem. An adversarially trained network and a sharpness detection network were trained to guide the training process. Experiments on both simulated and real dataset show that the results of the proposed method have very small resolution loss and achieves better performance relative to state-of-the-art methods both quantitatively and visually.

Aiding the Digital Mammogram for Detecting the Breast Cancer Using Shearlet Transform and Neural Network

Objective: Breast Cancer is the most invasive disease and fatal disease next to lung cancer in human. Early detection of breast cancer is accomplished by X-ray mammography. Mammography is the most effective and efficient technique used for detection of breast cancer in women and also to improve the breast cancer prognosis. The numbers of images need to be examined by the radiologists, the resulting may be misdiagnosis due to human errors by visual Fatigue. In order to avoid human errors, Computer Aided Diagnosis is implemented. In Computer Aided Diagnosis system, number of processing and analysis of an image is done by the suitable algorithm. Methods: This paper proposed a technique to aid radiologist to diagnosis breast cancer using Shearlet transform image enhancement method. Similar to wavelet filter, Shearlet coefficients are more directional sensitive than wavelet filters which helps detecting the cancer cells particularly for small contours. After enhancement of an image, segmentation algorithm is applied to identify the suspicious region. Result: Many features are extracted and utilized to classify the mammographic images into harmful or harmless tissues using neural network classifier. Conclusions: Multi-scale Shearlet transform because more details on data phase, directionality and shift invariance than wavelet based transforms. The proposed Shearlet transform gives multi resolution result and generate malign and benign classification more accurate up to 93.45% utilizing DDSM database.

Towards a Closed Form Second-Order Natural Scene Statistics Model

Previous work on natural scene statistics (NSS)-based image models has focused primarily on characterizing the univariate bandpass statistics of single pixels. These models have proven to be powerful tools driving a variety of computer vision and image/video processing applications, including depth estimation, image quality assessment, and image denoising, among others. Multivariate NSS models descriptive of the joint distributions of spatially separated bandpass image samples have, however, received relatively little attention. Here, we develop a closed form bivariate spatial correlation model of bandpass and normalized image samples that completes an existing 2D joint generalized Gaussian distribution model of adjacent bandpass pixels. Our model is built using a set of diverse, high-quality naturalistic photographs, and as a control, we study the model properties on white noise. We also study the way the model fits are affected when the images are modified by common distortions.

Infrared Aerial Small Target Detection with NSCT and Two-Dimensional Property Histogram

A novel algorithm is presented based on non-subsampled contourlet transform (NSCT) and two dimension property histogram in order to realize the aerial small target detection of infrared imaging under complex background. First, this method transforms the infrared image from space domain to NSCT domain. In high frequency bandpass domain, this method describes the sub-band coefficients according to Gaussian scale mixture model based on Bayesian estimation and estimates the center coefficient with the local neighbor’s in order to predict the high frequency background. On the other hand, this method predicts the low frequency background with self-adaption median filter in low frequency lowpass domain. Subsequently, the reversing NSCT is done and the complex background is estimated. By means of subtracting the estimated background image from the source image, the complex background is suppressed and the outstanding small target is acquired. Second, constructing the target’s property set according to the priori knowledge, this method defines the corresponding two-dimensional property histogram which is applied into calculating the segmenting threshold on basis of the maximum entropy method. Subsequently, the infrared image whose complex background is suppressed will be segmented into binary image by the threshold. Finally, infrared small target is detected by the pipeline filter algorithm which makes use of the relativity of the target movement between frames. The experimental results prove the presented method’s effectiveness which can detect the small target whose signal noise ratio (SNR) value is above 2 steadily.

Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain

The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson–Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson–Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.

Scale Invariant and Noise Robust Interest Points With Shearlets

Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities, such as edges and corners at multiple scales even in the presence of a large quantity of noise. In this paper, we consider blob-like features in the shearlets framework. We derive a measure, which is very effective for blob detection, and, based on this measure, we propose a blob detector and a keypoint description, whose combination outperforms the state-of-the-art algorithms with noisy and compressed images. We also demonstrate that the measure satisfies the perfect scale invariance property in the continuous case. We evaluate the robustness of our algorithm to different types of noise, including blur, compression artifacts, and Gaussian noise. Furthermore, we carry on a comparative analysis on benchmark data, referring, in particular, to tolerance to noise and image compression.

Comparison of contourlet transform and gray level co-occurrence matrix for analyzing cell-scattered patterns

Distribution of scattered image patterns hinges on morphological and optical characteristics of cells. This paper applied a numerical method to simulate scattered images of real cell morphologies, which were reconstructed from confocal image stacks dyed by fluorescent stains. Two approaches, contourlet transform (CT) and gray level co-occurrence matrix (GLCM), were then used to analyze the simulated scattered images. The results showed that features extracted using GLCM contained more information than those extracted using CT. Higher classification accuracy could be achieved with a single GLCM parameter than CT and GLCM could achieve higher accuracy with fewer parameters than CT when using multiple parameters. Meanwhile, GLCM requires less computational cost. Thus, GLCM is more suitable and efficient than CT for the analysis of cell-scattered images.

Edges and Corners With Shearlets

Shearlets are a relatively new and very effective multi-scale framework for signal analysis. Contrary to the traditional wavelets, shearlets are capable to efficiently capture the anisotropic information in multivariate problem classes. Therefore, shearlets can be seen as the valid choice for multi-scale analysis and detection of directional sensitive visual features like edges and corners. In this paper, we start by reviewing the main properties of shearlets that are important for edge and corner detection. Then, we study algorithms for multi-scale edge and corner detection based on the shearlet representation. We provide an extensive experimental assessment on benchmark data sets which empirically confirms the potential of shearlets feature detection.

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach.

Depth reconstruction from sparse samples: representation, algorithm, and sampling

The rapid development of 3D technology and computer vision applications has motivated a thrust of methodologies for depth acquisition and estimation. However, existing hardware and software acquisition methods have limited performance due to poor depth precision, low resolution, and high computational cost. In this paper, we present a computationally efficient method to estimate dense depth maps from sparse measurements. There are three main contributions. First, we provide empirical evidence that depth maps can be encoded much more sparsely than natural images using common dictionaries, such as wavelets and contourlets. We also show that a combined wavelet-contourlet dictionary achieves better performance than using either dictionary alone. Second, we propose an alternating direction method of multipliers (ADMM) for depth map reconstruction. A multiscale warm start procedure is proposed to speed up the convergence. Third, we propose a two-stage randomized sampling scheme to optimally choose the sampling locations, thus maximizing the reconstruction performance for a given sampling budget. Experimental results show that the proposed method produces high-quality dense depth estimates, and is robust to noisy measurements. Applications to real data in stereo matching are demonstrated.

Oriented correlation models of distorted natural images with application to natural stereopair quality evaluation

In recent years, bandpass statistical models of natural, photographic images of the world have been used with great success to solve highly diverse problems involving image representation, image repair, image quality assessment (IQA), and image compression. One missing element has been a reliable and generic model of spatial image correlation that reflects the distributions of oriented and relatively oriented spatial structures. We have developed such a model for bandpass pristine images and have generalized it here to also capture the spatial correlation structure of bandpass distorted images. The model applies well to both luminance and depth images. As a demonstration of the usefulness of the generalized model, we develop a new no-reference stereoscopic/3D IQA framework, dubbed stereoscopic/3D blind image naturalness quality index, which utilizes both univariate and generalized bivariate natural scene statistics (NSS) models. We first validate the robustness and effectiveness of these novel bivariate and correlation NSS features extracted from distorted stereopairs, then demonstrate that they are predictive of distortion severity. Our experimental results show that the resulting 3D image quality predictor based in part on the new model outperforms state-of-the-art full- and no-reference 3D IQA algorithms on both symmetrically and asymmetrically distorted stereoscopic image pairs.

Texture classification and retrieval using shearlets and linear regression

Statistical modeling of wavelet subbands has frequently been used for image recognition and retrieval. However, traditional wavelets are unsuitable for use with images containing distributed discontinuities, such as edges. Shearlets are a newly developed extension of wavelets that are better suited to image characterization. Here, we propose novel texture classification and retrieval methods that model adjacent shearlet subband dependences using linear regression. For texture classification, we use two energy features to represent each shearlet subband in order to overcome the limitation that subband coefficients are complex numbers. Linear regression is used to model the features of adjacent subbands; the regression residuals are then used to define the distance from a test texture to a texture class. Texture retrieval consists of two processes: the first is based on statistics in contourlet domains, while the second is performed using a pseudo-feedback mechanism based on linear regression modeling of shearlet subband dependences. Comprehensive validation experiments performed on five large texture datasets reveal that the proposed classification and retrieval methods outperform the current state-of-the-art.

Automated adjustment of region-based active contour parameters using local image geometry

A principled method for active contour (AC) parameterization remains a challenging issue in segmentation research, with a potential impact on the quality, objectivity, and robustness of the segmentation results. This paper introduces a novel framework for automated adjustment of region-based AC regularization and data fidelity parameters. Motivated by an isomorphism between the weighting factors of AC energy terms and the eigenvalues of structure tensors, we encode local geometry information by mining the orientation coherence in edge regions. In this light, the AC is repelled from regions of randomly oriented edges and guided toward structured edge regions. Experiments are performed on four state-of-the-art AC models, which are automatically adjusted and applied on benchmark datasets of natural, textured and biomedical images and two image restoration models. The experimental results demonstrate that the obtained segmentation quality is comparable to the one obtained by empirical parameter adjustment, without the cumbersome and time-consuming process of trial and error.

Coherence index and curvelet transformation for denoising geophysical data

Geophysical data contain stochastic noise that may mask their useful content. For example, ground roll (GR) is a coherent noise that is present in seismic data. Thus, such data are usually a mixture of useful information and useless coherent noise. The latter masks the relevant geologic information that seismic records contain, and its removal has always been a problem of fundamental importance. We propose a denoising method based on the curvelet transformation (CT), a multiscale transformation with strong directional character that provides an optimal representation of objects that have discontinuities along their edges. An algorithm is presented for processing and denoising of geophysical data. As an example, we apply the method to seismic images that are contaminated with the GR noise. First, the coherence index (CI), which represents a measure of the amount of energy contained in the most coherent modes of Karhunen-Lòeve transform for any given segment of the data, is computed. The contaminated region of the data is then identified as the maximum region of the CI. After demarcating the contaminated segment, the CT is used to eliminate the noise. The method removes the noise with negligible distortion of the data's noncontaminated region. It is also significantly more efficient computationallty than the previous methods. The use of the method is demonstrated by its application to synthetic, as well as actual, seismic data for hydrocarbon reservoirs.

A study of multiplicative watermark detection in the contourlet domain using alpha-stable distributions

In the past decade, several schemes for digital image watermarking have been proposed to protect the copyright of an image document or to provide proof of ownership in some identifiable fashion. This paper proposes a novel multiplicative watermarking scheme in the contourlet domain. The effectiveness of a watermark detector depends highly on the modeling of the transform-domain coefficients. In view of this, we first investigate the modeling of the contourlet coefficients by the alpha-stable distributions. It is shown that the univariate alpha-stable distribution fits the empirical data more accurately than the formerly used distributions, such as the generalized Gaussian and Laplacian, do. We also show that the bivariate alpha-stable distribution can capture the across scale dependencies of the contourlet coefficients. Motivated by the modeling results, a blind watermark detector in the contourlet domain is designed by using the univariate and bivariate alpha-stable distributions. It is shown that the detectors based on both of these distributions provide higher detection rates than that based on the generalized Gaussian distribution does. However, a watermark detector designed based on the alpha-stable distribution with a value of its parameter α other than 1 or 2 is computationally expensive because of the lack of a closed-form expression for the distribution in this case. Therefore, a watermark detector is designed based on the bivariate Cauchy member of the alpha-stable family for which α = 1 . The resulting design yields a significantly reduced-complexity detector and provides a performance that is much superior to that of the GG detector and very close to that of the detector corresponding to the best-fit alpha-stable distribution. The robustness of the proposed bivariate Cauchy detector against various kinds of attacks, such as noise, filtering, and compression, is studied and shown to be superior to that of the generalized Gaussian detector.

A Novel Approach for Image Enhancement via Nonsubsampled Contourlet Transform

An improved image enhancement approach via nonsubsampled contourlet transform (NSCT) is proposed in this article. We constructed a geometric image transform by combining nonsubsampled directional filter banks and a nonlinear mapping function. Here, the NSCT of the input image is first decomposed for L-levels and its noise standard deviation is estimated. It is followed by calculating the noise variance and threshold calculation, and computing the magnitude of the corresponding coefficients in all directional subbands. Then, the nonlinear mapping function is used to modify the NSCT coefficients for each directional subband, which keeps the coefficients of strong edges, amplifies the coefficients of weak edges, and zeros the noise coefficients. Finally, the enhanced image is reconstructed from the modified NSCT coefficients. Three experiments are carried out respectively on images from subjective vision quality and objective evaluation measures. The first experiment is the algorithm performed on images. The subsequent experiments are the information entropy and spatial frequency. The experimental results demonstrate that the proposed method can gain better performance in enhancing the low-contrast parts of an image while keeping its clear edges.

Gaussian Copula multivariate modeling for texture image retrieval using wavelet transforms

In the framework of texture image retrieval, a new family of stochastic multivariate modeling is proposed based on Gaussian Copula and wavelet decompositions. We take advantage of the copula paradigm, which makes it possible to separate dependence structure from marginal behavior. We introduce two new multivariate models using, respectively, generalized Gaussian and Weibull densities. These models capture both the subband marginal distributions and the correlation between wavelet coefficients. We derive, as a similarity measure, a closed form expression of the Jeffrey divergence between Gaussian copula-based multivariate models. Experimental results on well-known databases show significant improvements in retrieval rates using the proposed method compared with the best known state-of-the-art approaches.

Rotation-Covariant Texture Learning Using Steerable Riesz Wavelets

We propose a texture learning approach that exploits local organizations of scales and directions. First, linear combinations of Riesz wavelets are learned using kernel support vector machines. The resulting texture signatures are modeling optimal class-wise discriminatory properties. The visualization of the obtained signatures allows verifying the visual relevance of the learned concepts. Second, the local orientations of the signatures are optimized to maximize their responses, which is carried out analytically and can still be expressed as a linear combination of the initial steerable Riesz templates. The global process is iteratively repeated to obtain final rotation-covariant texture signatures. Rapid convergence of class-wise signatures is observed, which demonstrates that the instances are projected into a feature space that leverages the local organizations of scales and directions. Experimental evaluation reveals average classification accuracies in the range of 97% to 98% for the Outex_TC_00010, the Outex_TC_00012, and the Contrib_TC_00000 suites for even orders of the Riesz transform, and suggests high robustness to changes in images orientation and illumination. The proposed framework requires no arbitrary choices of scales and directions and is expected to perform well in a large range of computer vision applications.

Bayesian learning of sparse multiscale image representations

Multiscale representations of images have become a standard tool in image analysis. Such representations offer a number of advantages over fixed-scale methods, including the potential for improved performance in denoising, compression, and the ability to represent distinct but complementary information that exists at various scales. A variety of multiresolution transforms exist, including both orthogonal decompositions such as wavelets as well as nonorthogonal, overcomplete representations. Recently, techniques for finding adaptive, sparse representations have yielded state-of-the-art results when applied to traditional image processing problems. Attempts at developing multiscale versions of these so-called dictionary learning models have yielded modest but encouraging results. However, none of these techniques has sought to combine a rigorous statistical formulation of the multiscale dictionary learning problem and the ability to share atoms across scales. We present a model for multiscale dictionary learning that overcomes some of the drawbacks of previous approaches by first decomposing an input into a pyramid of distinct frequency bands using a recursive filtering scheme, after which we perform dictionary learning and sparse coding on the individual levels of the resulting pyramid. The associated image model allows us to use a single set of adapted dictionary atoms that is shared--and learned--across all scales in the model. The underlying statistical model of our proposed method is fully Bayesian and allows for efficient inference of parameters, including the level of additive noise for denoising applications. We apply the proposed model to several common image processing problems including non-Gaussian and nonstationary denoising of real-world color images.

Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage

Speckle reduction of retinal optical coherence tomography (OCT) images helps the diagnosis of ocular diseases. In this Letter, we present a speckle reduction method based on shrinkage in the contourlet domain for retinal OCT images. The algorithm overcomes the disadvantages of the wavelet shrinkage method, which lacks directionality and anisotropy. The trade-off between speckle reduction and edge preservation is controlled by a single adjustable parameter, which determines the threshold in the contourlet domain. Results show substantial reduction of speckle noise and enhanced visualization of layer structures as demonstrated in the image of the central fovea region of the human retina. It is expected to be utilized in a wide range of biomedical imaging applications.

A REVIEW OF WAVELET-BASED EDGE DETECTION METHODS

Edges are prominent features in images. The detection and analysis of edges are key issues in image processing, computer vision and pattern recognition. Wavelet provides a powerful tool to analyze the local regularity of signals. Wavelet transform has been successfully applied to the analysis and detection of edges. A great number of wavelet-based edge detection methods have been proposed over the past years. The objective of this paper is to give a brief review of these methods, and encourage the research of this topic. In practice, an image is usually of multistructure edge, the identification of different edges, such as steps, curves and junctions play an important role in pattern recognition. In this paper, more attention is paid on the identification of different types of edges. We present the main idea and the properties of these methods.

Improved Rotating Kernel Transformation Based Contourlet Domain Image Denoising Framework

A contourlet domain image denoising framework based on a novel Improved Rotating Kernel Transformation is proposed, where the difference of subbands in contourlet domain is taken into account. In detail: (1). A novel Improved Rotating Kernel Transformation (IRKT) is proposed to calculate the direction statistic of the image; The validity of the IRKT is verified by the corresponding extracted edge information comparing with the state-of-the-art edge detection algorithm. (2). The direction statistic represents the difference between subbands and is introduced to the threshold function based contourlet domain denoising approaches in the form of weights to get the novel framework. The proposed framework is utilized to improve the contourlet soft-thresholding (CTSoft) and contourlet bivariate-thresholding (CTB) algorithms. The denoising results on the conventional testing images and the Optical Coherence Tomography (OCT) medical images show that the proposed methods improve the existing contourlet based thresholding denoising algorithm, especially for the medical images.

Wavelet modeling using finite mixtures of generalized gaussian distributions: application to texture discrimination and retrieval

This paper addresses statistical-based texture modeling using wavelets. We propose a new approach to represent the marginal distribution of the wavelet coefficients using finite mixtures of generalized Gaussian (MoGG) distributions. The MoGG captures a wide range of histogram shapes, which provides better description and discrimination of texture than using single probability density functions (pdf's), as proposed by recent state-of-the-art approaches. Moreover, we propose a model similarity measure based on Kullback-Leibler divergence (KLD) approximation using Monte Carlo sampling methods. Through experiments on two popular texture data sets, we show that our approach yields significant performance improvements for texture discrimination and retrieval, as compared with recent methods of statistical-based wavelet modeling.

Bayesian texture classification based on contourlet transform and BYY harmony learning of Poisson mixtures

As a newly developed 2-D extension of the wavelet transform using multiscale and directional filter banks, the contourlet transform can effectively capture the intrinsic geometric structures and smooth contours of a texture image that are the dominant features for texture classification. In this paper, we propose a novel Bayesian texture classifier based on the adaptive model-selection learning of Poisson mixtures on the contourlet features of texture images. The adaptive model-selection learning of Poisson mixtures is carried out by the recently established adaptive gradient Bayesian Ying-Yang harmony learning algorithm for Poisson mixtures. It is demonstrated by the experiments that our proposed Bayesian classifier significantly improves the texture classification accuracy in comparison with several current state-of-the-art texture classification approaches.

Critically sampled wavelets with composite dilations

Wavelets with composite dilations provide a general framework for the construction of waveforms defined not only at various scales and locations, as traditional wavelets, but also at various orientations and with different scaling factors in each coordinate. As a result, they are useful to analyze the geometric information that often dominate multidimensional data much more efficiently than traditional wavelets. The shearlet system, for example, is a particular well-known realization of this framework, which provides optimally sparse representations of images with edges. In this paper, we further investigate the constructions derived from this approach to develop critically sampled wavelets with composite dilations for the purpose of image coding. Not only do we show that many nonredundant directional constructions recently introduced in the literature can be derived within this setting, but we also introduce new critically sampled discrete transforms that achieve much better nonlinear approximation rates than traditional discrete wavelet transforms and outperform the other critically sampled multiscale transforms recently proposed.

OPTICAL COHERENCE TOMOGRAPHY HEART TUBE IMAGE DENOISING BASED ON CONTOURLET TRANSFORM

Optical Coherence Tomography(OCT) gradually becomes a very important imaging technology in the Biomedical field for its noninvasive, nondestructive and real-time properties. However, the interpretation and application of the OCT images are limited by the ubiquitous noise. In this paper, a denoising algorithm based on contourlet transform for the OCT heart tube image is proposed. A bivariate function is constructed to model the joint probability density function (pdf) of the coefficient and its cousin in contourlet domain. A bivariate shrinkage function is deduced to denoise the image by the maximum a posteriori (MAP) estimation. Three metrics, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and equivalent number of look (ENL), are used to evaluate the denoised image using the proposed algorithm. The results show that the signal-to-noise ratio is improved while the edges of object are preserved by the proposed algorithm. Systemic comparisons with other conventional algorithms, such as mean filter, median filter, RKT filter, Lee filter, as well as bivariate shrinkage function for wavelet-based algorithm are conducted. The advantage of the proposed algorithm over these methods is illustrated.