Curvelets and Ridgelets

International audienceDespite the fact that wavelets have had a wide impact in image processing, they fail to efficiently represent objects with highly anisotropic elements such as lines or curvilinear structures (e.g. edges). The reason is that wavelets are non-geometrical and do not exploit the regularity of the edge curve. The Ridgelet and the Curvelet [3, 4] transforms were developed as an answer to the weakness of the separable wavelet transform in sparsely representing what appears to be simple building atoms in an image, that is lines, curves and edges. Curvelets and ridgelets take the form of basis elements which exhibit high directional sensitivity and are highly anisotropic [5, 6, 7, 8]. These very recent geometric image representations are built upon ideas of multiscale analysis and geometry. They have had an important success in a wide range of image processing applications including denoising [8, 9, 10], deconvolution [11, 12], contrast enhancement [13], texture analysis [14, 15], detection [16], watermarking [17], component separation [18], inpainting [19, 20] or blind source separation[21, 22]. Curvelets have also proven useful in diverse fields beyond the traditional image processing application. Let’s cite for example seismic imaging [10, 23, 24], astronomical imaging [25, 26, 27], scientific computing and analysis of partial differential equations [28, 29]. Another reason for the success of ridgelets and curvelets is the availability of fast transform algorithms which are available in non-commercial software packages following the philosophy of reproducible research, see [30, 31]

New algorithms for the analysis of live-cell images acquired in phase contrast microscopy

La détection et la caractérisation automatisée des cellules constituent un enjeu important dans de nombreux domaines de recherche tels que la cicatrisation, le développement de l'embryon et des cellules souches, l’immunologie, l’oncologie, l'ingénierie tissulaire et la découverte de nouveaux médicaments. Étudier le comportement cellulaire in vitro par imagerie des cellules vivantes et par le criblage à haut débit implique des milliers d'images et de vastes quantités de données. Des outils d'analyse automatisés reposant sur la vision numérique et les méthodes non-intrusives telles que la microscopie à contraste de phase (PCM) sont nécessaires. Comme les images PCM sont difficiles à analyser en raison du halo lumineux entourant les cellules et de la difficulté à distinguer les cellules individuelles, le but de ce projet était de développer des algorithmes de traitement d'image PCM dans Matlab® afin d’en tirer de l’information reliée à la morphologie cellulaire de manière automatisée. Pour développer ces algorithmes, des séries d’images de myoblastes acquises en PCM ont été générées, en faisant croître les cellules dans un milieu avec sérum bovin (SSM) ou dans un milieu sans sérum (SFM) sur plusieurs passages. La surface recouverte par les cellules a été estimée en utilisant un filtre de plage de valeurs, un seuil et une taille minimale de coupe afin d'examiner la cinétique de croissance cellulaire. Les résultats ont montré que les cellules avaient des taux de croissance similaires pour les deux milieux de culture, mais que celui-ci diminue de façon linéaire avec le nombre de passages. La méthode de transformée par ondelette continue combinée à l’analyse d'image multivariée (UWT-MIA) a été élaborée afin d’estimer la distribution de caractéristiques morphologiques des cellules (axe majeur, axe mineur, orientation et rondeur). Une analyse multivariée réalisée sur l’ensemble de la base de données (environ 1 million d’images PCM) a montré d'une manière quantitative que les myoblastes cultivés dans le milieu SFM étaient plus allongés et plus petits que ceux cultivés dans le milieu SSM. Les algorithmes développés grâce à ce projet pourraient être utilisés sur d'autres phénotypes cellulaires pour des applications de criblage à haut débit et de contrôle de cultures cellulaires.Automated cell detection and characterization is important in many research fields such as wound healing, embryo development, immune system studies, cancer research, parasite spreading, tissue engineering, stem cell research and drug research and testing. Studying in vitro cellular behavior via live-cell imaging and high-throughput screening involves thousands of images and vast amounts of data, and automated analysis tools relying on machine vision methods and non-intrusive methods such as phase contrast microscopy (PCM) are a necessity. However, there are still some challenges to overcome, since PCM images are difficult to analyze because of the bright halo surrounding the cells and blurry cell-cell boundaries when they are touching. The goal of this project was to develop image processing algorithms to analyze PCM images in an automated fashion, capable of processing large datasets of images to extract information related to cellular viability and morphology. To develop these algorithms, a large dataset of myoblasts images acquired in live-cell imaging (in PCM) was created, growing the cells in either a serum-supplemented (SSM) or a serum-free (SFM) medium over several passages. As a result, algorithms capable of computing the cell-covered surface and cellular morphological features were programmed in Matlab®. The cell-covered surface was estimated using a range filter, a threshold and a minimum cut size in order to look at the cellular growth kinetics. Results showed that the cells were growing at similar paces for both media, but their growth rate was decreasing linearly with passage number. The undecimated wavelet transform multivariate image analysis (UWT-MIA) method was developed, and was used to estimate cellular morphological features distributions (major axis, minor axis, orientation and roundness distributions) on a very large PCM image dataset using the Gabor continuous wavelet transform. Multivariate data analysis performed on the whole database (around 1 million PCM images) showed in a quantitative manner that myoblasts grown in SFM were more elongated and smaller than cells grown in SSM. The algorithms developed through this project could be used in the future on other cellular phenotypes for high-throughput screening and cell culture control applications

A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain

Detecting camouflaged moving foreground objects has been known to be difficult due to the similarity between the foreground objects and the background. Conventional methods cannot distinguish the foreground from background due to the small differences between them and thus suffer from under-detection of the camouflaged foreground objects. In this paper, we present a fusion framework to address this problem in the wavelet domain. We first show that the small differences in the image domain can be highlighted in certain wavelet bands. Then the likelihood of each wavelet coefficient being foreground is estimated by formulating foreground and background models for each wavelet band. The proposed framework effectively aggregates the likelihoods from different wavelet bands based on the characteristics of the wavelet transform. Experimental results demonstrated that the proposed method significantly outperformed existing methods in detecting camouflaged foreground objects. Specifically, the average F-measure for the proposed algorithm was 0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI

Wavelet-Based Enhancement Technique for Visibility Improvement of Digital Images

Image enhancement techniques for visibility improvement of color digital images based on wavelet transform domain are investigated in this dissertation research. In this research, a novel, fast and robust wavelet-based dynamic range compression and local contrast enhancement (WDRC) algorithm to improve the visibility of digital images captured under non-uniform lighting conditions has been developed. A wavelet transform is mainly used for dimensionality reduction such that a dynamic range compression with local contrast enhancement algorithm is applied only to the approximation coefficients which are obtained by low-pass filtering and down-sampling the original intensity image. The normalized approximation coefficients are transformed using a hyperbolic sine curve and the contrast enhancement is realized by tuning the magnitude of the each coefficient with respect to surrounding coefficients. The transformed coefficients are then de-normalized to their original range. The detail coefficients are also modified to prevent edge deformation. The inverse wavelet transform is carried out resulting in a lower dynamic range and contrast enhanced intensity image. A color restoration process based on the relationship between spectral bands and the luminance of the original image is applied to convert the enhanced intensity image back to a color image. Although the colors of the enhanced images produced by the proposed algorithm are consistent with the colors of the original image, the proposed algorithm fails to produce color constant results for some pathological scenes that have very strong spectral characteristics in a single band. The linear color restoration process is the main reason for this drawback. Hence, a different approach is required for tackling the color constancy problem. The illuminant is modeled having an effect on the image histogram as a linear shift and adjust the image histogram to discount the illuminant. The WDRC algorithm is then applied with a slight modification, i.e. instead of using a linear color restoration, a non-linear color restoration process employing the spectral context relationships of the original image is applied. The proposed technique solves the color constancy issue and the overall enhancement algorithm provides attractive results improving visibility even for scenes with near-zero visibility conditions. In this research, a new wavelet-based image interpolation technique that can be used for improving the visibility of tiny features in an image is presented. In wavelet domain interpolation techniques, the input image is usually treated as the low-pass filtered subbands of an unknown wavelet-transformed high-resolution (HR) image, and then the unknown high-resolution image is produced by estimating the wavelet coefficients of the high-pass filtered subbands. The same approach is used to obtain an initial estimate of the high-resolution image by zero filling the high-pass filtered subbands. Detail coefficients are estimated via feeding this initial estimate to an undecimated wavelet transform (UWT). Taking an inverse transform after replacing the approximation coefficients of the UWT with initially estimated HR image, results in the final interpolated image. Experimental results of the proposed algorithms proved their superiority over the state-of-the-art enhancement and interpolation techniques

Sparsity and adaptivity for the blind separation of partially correlated sources

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin

Image Restoration: A General Wavelet Frame Based Model and Its Asymptotic Analysis

Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a generic wavelet frame based image restoration model, called the "general model", which includes most of the existing wavelet frame based models as special cases. Moreover, the general model also includes examples that are new to the literature. Motivated by our earlier studies [1-3], We provide an asymptotic analysis of the general model as image resolution goes to infinity, which establishes a connection between the general model in discrete setting and a new variatonal model in continuum setting. The variational model also includes some of the existing variational models as special cases, such as the total generalized variational model proposed by [4]. In the end, we introduce an algorithm solving the general model and present one numerical simulation as an example

Comparison of DCT, SVD and BFOA based multimodal biometric watermarking systems

AbstractDigital image watermarking is a major domain for hiding the biometric information, in which the watermark data are made to be concealed inside a host image imposing imperceptible change in the picture. Due to the advance in digital image watermarking, the majority of research aims to make a reliable improvement in robustness to prevent the attack. The reversible invisible watermarking scheme is used for fingerprint and iris multimodal biometric system. A novel approach is used for fusing different biometric modalities. Individual unique modalities of fingerprint and iris biometric are extracted and fused using different fusion techniques. The performance of different fusion techniques is evaluated and the Discrete Wavelet Transform fusion method is identified as the best. Then the best fused biometric template is watermarked into a cover image. The various watermarking techniques such as the Discrete Cosine Transform (DCT), Singular Value Decomposition (SVD) and Bacterial Foraging Optimization Algorithm (BFOA) are implemented to the fused biometric feature image. Performance of watermarking systems is compared using different metrics. It is found that the watermarked images are found robust over different attacks and they are able to reverse the biometric template for Bacterial Foraging Optimization Algorithm (BFOA) watermarking technique