Stéphanie Jehan-Besson

Region-Based Active Contours with Exponential Family Observations

In this paper, 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. In the framework developed in this paper, we consider the general case of region-based terms involving functions of parametric probability densities, for which the anti-log-likelihood function is a special case. Using shape derivative tools, our effort focuses on constructing a general expression for the derivative of the energy (with respect to a domain), and on deriving the corresponding evolution speed. More precisely, we first show by an example that the estimator of the distribution parameters is crucial for the derived speed expression. On the one hand, when using the maximum likelihood (ML) estimator for these parameters, the evolution speed has a closed-form expression that depends simply on the probability density function. On the other hand, complicating additive terms appear when using other estimators, e.g. method of moments. We then proceed by stating a general result within the framework of multi-parameter exponential family. This result is specialized to the case of the anti-log-likelihood function with the ML estimator and to the case of the relative entropy. Experimental results on simulated data confirm our expectations that using the appropriate noise model leads to the best segmentation performance. We also report preliminary experiments on real life Synthetic Aperture Radar (SAR) images to demonstrate the potential applicability of our approach.

An Augmented Lagrangian Method for TVg+L1-norm Minimization

In this paper, the minimization of a weighted total variation regularization term (denoted TVg) with L1 norm as the data fidelity term is addressed using the Uzawa block relaxation method. The unconstrained minimization problem is transformed into a saddle-point problem by introducing a suitable auxiliary unknown. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional, we obtain a new numerical algorithm in which the main unknown is computed using Chambolle projection algorithm. The auxiliary unknown is computed explicitly. Numerical experiments show the availability of our algorithm for salt and pepper noise removal or shape retrieval and also its robustness against the choice of the penalty parameter. This last property is useful to attain the convergence in a reduced number of iterations leading to efficient numerical schemes. The specific role of the function g in TVg is also investigated and we highlight the fact that an appropriate choice leads to a significant improvement of the denoising results. Using this property, we propose a whole algorithm for salt and pepper noise removal (denoted UBR-EDGE) that is able to handle high noise levels at a low computational cost. Shape retrieval and geometric filtering are also investigated by taking into account the geometric properties of the model.

Significance Tests and Statistical Inequalities for Region Matching

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 paper, 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.

Optimization of Divergences within the Exponential Family for Image Segmentation

In this work, we propose novel results for the optimization of divergences within the framework of region-based active contours. We focus on parametric statistical models where the region descriptor is chosen as the probability density function (pdf) of an image feature (e.g. intensity) inside the region and the pdf belongs to the exponential family. The optimization of divergences appears as a flexible tool for segmentation with and without intensity prior. As far as segmentation without reference is concerned, we aim at maximizing the discrepancy between the pdf of the inside region and the pdf of the outside region. Moreover, since the optimization framework is performed within the exponential family, we can cope with difficult segmentation problems including various noise models (Gaussian, Rayleigh, Poisson, Bernoulli ...). We also experimentally show that the maximisation of the KL divergence offers interesting properties compare to some other data terms (e.g. minimization of the anti-log-likelihood). Experimental results on medical images (brain MRI, contrast echocardiography) confirm the applicability of this general setting.

A mutual reference shape based on information theory

In this paper, we consider the estimation of a reference shape from a set of different segmentation results using both active contours and information theory. The reference shape is defined as the minimum of a criterion that benefits from both the mutual information and the joint entropy of the input segmentations and is then called a mutual shape. This energy criterion is here justified using similarities between information theory quantities and area measures, and presented in a continuous variational framework. This framework brings out some interesting evaluation measures such as the specificity and sensitivity. In order to solve this shape optimization problem, shape derivatives are computed for each term of the criterion and interpreted as an evolution equation of an active contour. Some synthetical examples allow us to cast the light on the difference between our mutual shape and an average shape. Our framework has been considered for the estimation of a mutual shape for the evaluation of cardiac segmentation methods in MRI.

Comparison of 2D and 3D region-based deformable models and random walker methods for PET segmentation

In this paper, we propose to compare different methods for tumor segmentation in positron emission tomography (PET) images. We first propose to tackle this problem under the umbrella of shape optimization and 3D deformable models. Indeed, 2D active contours have been widely investigated in the literature but these techniques do not take advantage of 3D informations. On the one hand, we use the well-known model of Chan and Vese. On the other hand we use a criterion based on parametric probabilities which allows us to test the assumption of Poisson distribution of the intensity in such images. Both will be compared to their 2D equivalent and to an improved random-walker algorithm. For this comparison, we use a set of simulated, phantom and real sequences with a known ground-truth and compute the corresponding Dice Coefficients. We also give some examples of 2D and 3D segmentation results.