Estimation, detection and pattern recognition

Region matching - finding conjugate regions on a pair of images - plays a fundamental role in computer vision. Indeed, such methods have numerous applications such as indexation, motion estimation or tracking. In the vast literature on the subject, several dissimilarity measures have been proposed in order to determine the true match for each region. In this work, under statistical hypothesis of similarity, we provide an improved decision rule for patch matching based on significance tests and the statistical inequality of McDiarmid.

The proposed decision rule allows to validate or not the similarity hypothesis and so to automatically detect matching outliers. The approach is applied to motion estimation and object tracking on noisy video sequences. Note that the proposed framework is robust against noise, avoids the use of statistical tests and may be related to the a contrario approach.

Deconvolution consists in the inversion of the degradation process of the acquisition system. This degradation is generally due to the optic system which introduces blur and the probe which introduce noises. We propose a novel method for restauring such images using an a priori of sparsity into a wavelet domain of the original image. The algorithm lies on the minimization of two terms: the fidelity term (which describes the degradation process) and the l1 norm of the wavelets' coefficients (which promotes sparsity). A toolbox illustrating this method is avaible for Matlab (require WaveLab802).

It is often necessary to identify and quantify cell and tissue compartments on histological sections, to estimate the potential evolution of the cancer lesions. To perform this measure, in an objective way, an image of the whole preparation (so-called Virtual Slide, VS) must be recorded and fully analyzed, as structures of interest are often heterogeneously spread all over the slide. It is also mandatory to adapt the working resolution to the size of the structures to be measured. High resolution VS produced for the identification of tiny microscopical structures occupy a very large volume in memory (several GigaBytes) and cannot be processed at once. The method chosen by our team is a multiscale analysis of a high resolution VS, allowing to adapt the working resolution to the various structures to be segmented.

The study aims first at partitioning cancer cells and intra tumoral connective tissue inside VS of ovarian carcinomas, recorded at a high resolution (0.5 ?m), and then at differentiating the various stromal compartments (fibrous tissue, loose mesenchymatous connective tissue, inflammatory cell accumulation). Stromal compartments can be identified mainly by their cell shape and organization. Then, each stromal component must exhibit an individual pattern which has to be characterized by texture analysis.

We chose to use the Hidden Markov Tree (HMT) proposed by Crouse. It allows a statistical modeling of intra-scale and interscale properties of coefficients obtained by wavelet transform (WT). The goal is to capture the interscale dependency factor and the non-gaussian distribution of the coefficients computed at each scale. This model is applied to the segmentation of the various compartments of stroma.

The HMT parameters are calculated through a learning set of pure class images, for each combination of the method parameters : the wavelet base, the color image component on which the WT is applied and the number of resolution levels on which the analysis is focused. Each set of hyper-parameters allows to generate a different segmentation and corresponds to a classifier. To merge the outputs of the classifiers, we use the majority vote combination rule.

We succeed to segment 60000x40000 pixels images and the results are promising.

We present a robust method to retrieve neuronal fibers in human brain white matter from High-Angular Resolution MRI (HARDI datasets). Contrary to classical fiber-tracking techniques done on the traditional 2nd-order tensor model (DTI) which may lead to truncated or biased estimated diffusion directions in case of fiber crossing configurations, we propose here a more complex approach based on a variational estimation of Orientation Diffusion Functions (ODF) modeled with spherical harmonics. This kind of model can correctly retrieve multiple fiber directions corresponding to underlying intravoxel fibers populations. Our technique is able to consider the Rician noise model of the MRI acquisition in order to better estimate the white matter fiber tracks. Results on both synthetic and real human brain white matter HARDI datasets illustrate the effectiveness of the proposed approach.

The current work is devoted to the segmentation of regions with a priori known shape in noisy images using region-based active contours. This method allows the use of photometric image properties, such as texture and noise, as well as geometric properties such as the shape of the object to be segmented. The shape prior can prove very useful in cases where the object is occluded or partially missing. Furthermore, if one knows the degradation model of the images, and have an access to their noise model, the noise model can also be added. Experimental results on both synthetic images and real life cardiac echography data clearly demonstrate the robustness to initialization and noise, versatility and large potential applicability of our segmentation algorithm.

We focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to the special Gaussian case. Using shape derivation tools, our effort focuses on constructing a general expression for the derivative of the energy (with respect to a domain) and derive the corresponding evolution speed. A general result is stated within the framework of multi-parameter exponential family. More particularly, when using Maximum Likelihood estimators, the evolution speed has a closed-form expression that depends simply on the probability density function, while complicating additive terms appear when using other estimators, e.g. moments method. Experimental results on both synthesized and real images demonstrate the applicability of our approach.

We are interested in the reconstruction of missing data in color images, by the means of spatial interpolations that preserve textures. This so-called "inpainting" process has several applications in the field of image processing. We propose a two-step algorithm for this purpose~: first, we reconstruct the image isophotes in missing data regions using multi-valued PDE's that perform anisotropic smoothing. Then, we synthetize the missing textures therein using a smart bloc matching scheme. Finally, we illustrate our algorithm for real objects removal in color photographs.

We are interested in PDE's (Partial Differential Equations) in order to smooth multi-valued images in an anisotropic manner. We introduce a new tensor-driven PDE, regularizing images while taking the curvatures of specific integral curves into account. We show that this constraint is particularly well suited for image restoration purposes. A direct link is made between our proposed equation and a continuous formulation of the LIC's (Line Integral Convolutions). It leads to the design of a very fast and stable algorithm that implements our regularization method. Besides, the important rotational invariance property of the scheme is ensured from a numerical point of view, which is not the case with classical finite-differences discretizations. We illustrate the efficiency of our generic curvature-preserving approach - in terms of speed and visual quality - with different comparisons and various applications requiring image smoothing~: color images denoising, inpainting and image resizing by nonlinear interpolation.

Inpainting is to restore missing image information based upon the still available (observed) cues. We have introduced an expectation-maximization (EM) algorithm for image inpainting based on a penalized likelihood formulated using linear sparse representations. Taking advantage of the sparsity of representations, a regularization through a prior penalty is imposed on the reconstructed coefficients. From a statistical point of view, the inpainting can be viewed as an estimation problem with missing data. The EM framework is a general iterative algorithm for ML estimation in such situations. The EM framework gives a principled way to establish formally the idea that missing samples can be recovered based on sparse representations. Furthermore, owing to its well known theoretical properties, the EM algorithm allows to investigate the convergence behavior of the inpainting algorithm. The EMInpaint software was developed for 2D images under Matlab (requires WaveLab802) and Pandore (C++) environements.

We recently proposed a multi-scale framework for spatio-temporal data analysis and modelling, with a specific application to functional MRI of the brain. The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or whitening of a wide class of processes which are beyond the classical stationary and short-term assumption. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We here provide a brief review of our work on its application to fMRI. We focus on these applications in particular: (i) wavelet-based structural and random fluctuations modelling, (ii) wavelet coefficient resampling or wavestrapping of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes, (iii) wavelet-based estimators for parametric and semiparametric models; and (iv) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. The wavelet-base multiscale framework is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.

Morphological Component Analysis is a novel tool for semi-blind semantic components separation for signals and images, e.g. locally oscillating and piece-wise regular parts. For example, one could be interested in separating the texture from non texture in an image, or wants to get the filamentary structures embedded in an image, etc. The separation can be accomplished while jointly rejecting the noise.

MCA brings together tools from harmonic analysis, statistics and optimization theory to solve the separation/restoration problem. The key idea behind the MCA is that one is able to construct a dictionary composed of two or more representations where each semantic component of the image is sparsely represented. As an illustrative example, for the texture vs BV component, one can use respectively the local DCT and the wavelet representations in the dictionary. The MCA software was developed for both 1D signals and 2D images under Matlab (requires WaveLab802) and Pandore (C++) environements.

We assess the performance of our Bayesian denoiser with the scale-mixture approximation to the alpha-stable prior, called alpha-stable mixture, and we compare it to other previously published denoising methods. For the comparaison to be fair, we only chose denoising methods using the same transforms, namely, the DWT. Extension to overcomplete representations which are translation and rotation invariant are the subject of our ongoing research. Six other denoising algorithms are considered: the universal threshold Hard and Soft thresholding, the Stein Unbiased Risk Estimator (SURE), the Oracle threshold estimator (Oracle), the Bessel K forms (BKF) Bayesian denoiser and the original version of the alpha-stable Bayesian denoiser. In the latter, no closed-form is available for the PCM Bayesian denoiser. We here used an equivalent form involving Fourier integrals. The numerically Fourier integrals were implemented using FFT-based methods.