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.

A statistical methodology is proposed to rank several estimation methods of a relevant clinical parameter when no gold standard is available. Based on a regression without truth method, the proposed approach was applied to rank eight methods without using any a priori information regarding the reliability of each method and its degree of automation. It was only based on a prior concerning the statistical distribution of the parameter of interest in the database. The ranking of the methods relies on figures of merit derived from the regression and computed using a bootstrap process. The methodology was applied to the estimation of the left ventricular ejection fraction derived from cardiac magnetic resonance images segmented using eight approaches with different degrees of automation: three segmentations were entirely manually performed and the others were variously automated. The ranking of methods was consistent with the expected performance of the estimation methods: the most accurate estimates of the ejection fraction were obtained using manual segmentations. The robustness of the ranking was demonstrated when at least three methods were compared. These results suggest that the proposed statistical approach might be helpful to assess the performance of estimation methods on clinical data for which no gold standard is available.

In this paper we propose a rigorous framework for texture image segmentation relying on region-based active contours (RBAC) and sparse texture representation. Such representations allow to efficiently describe a texture by transforming it in a dictionary of appropriate waveforms (atoms) where the texture representation coefficients are concentrated on a small set. For segmentation purposes. these atoms have to be multiscale and localized both in space and frequency, e.g. the wavelet transform. To discriminate different textures, we measure a ldquodistancerdquo between the non-parametric Parzen estimates of their respective sparse-representation coefficients probability density functions (pdfs). These distance measures are then used within RBAC, and we take benefit from shape derivative tools to derive the evolution speed expression of the RBAC. Our framework is applied to both supervised (with reference textures), and unsupervised texture segmentation. A series of experiments on synthetic textures illustrate the potential applicability of our method.

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. 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

In this paper, we propose to combine formally noise and shape priors in region-based active contours. On the one hand, we use the general framework of exponential family as a prior model for noise. On the other hand, translation and scale invariant Legendre moments are considered to incorporate the shape prior (e.g. fidelity to a reference shape). The combination of the two prior terms in the active contour functional yields the final evolution equation whose evolution speed is rigorously derived using shape derivative tools. Experimental results on both synthetic images and real life cardiac echography data clearly demonstrate the robustness to initialization and noise, flexibility and large potential applicability of our segmentation algorithm.

The paper deals with video and image segmentation using region based active contours. We consider the problem of segmentation through the minimization of a new criterion based on information theory. We first propose to derive a general criterion based on the probability density function using the notion of shape gradient. This general derivation is then applied to criteria based on information theory, such as the entropy or the conditional entropy for the segmentation of sequences of images. We present experimental results on grayscale images and color videos showing the accuracy of the proposed method.

We consider the problem of image segmentation using active contours through the minimization of an energy criterion involving both region and boundary functionals. These functionals are derived through a shape derivative approach instead of classical calculus of variation. The equations can be elegantly derived without converting the region integrals into boundary integrals. From the derivative, we deduce the evolution equation of an active contour that makes it evolve towards a minimum of the criterion. We focus more particularly on statistical features globally attached to the region and especially to the probability density functions of image features such as the color histogram of a region. A theoretical framework is set for the minimization of the distance between two histograms for matching or tracking purposes. An application of this framework to the segmentation of color histograms in video sequences is then proposed. We briefly describe our numerical scheme and show some experimental results.

The problem of image segmentation through the minimization of an energy criterion involving both region and boundary functionals is considered. We study the derivation of these functionals using the notion of shape derivative. From the derivative, we deduce the evolution equation of an active contour that will make it evolve towards a minimum of the criterion introduced. We focus on geometric and statistical features globally attached to the boundary or to the region, and we take explicitly into account their evolution in the derivation. First, statistical region-based descriptors using the variance of a region or the distance to a reference region histogram are introduced. Then a geometric prior term is combined with statistical features for homogeneous region segmentation. This geometric prior is introduced to provide a free form deformation from a reference shape. Some experimental results on real images and video sequences show the benefit of combining geometrical and statistical features for segmentation.

We present a new algorithm for the segmentation of moving objects in a video sequence acquired by a mobile camera using region-based active contours. Indeed, active contours are powerful tools for segmentation. However, as far as segmentation of moving objects is concerned, region-based terms must be incorporated in the evolution equation, in addition to classical boundary-based terms. We consequently propose a general framework for region-based active contours with a new Eulerian method to compute the evolution equation of the active contour. This general framework is then applied to the segmentation of moving objects from a sequence with a moving camera. We propose to jointly perform camera compensation and segmentation by taking directly into account the camera model in the criterion to minimize.

In order to improve efficiency of video coding, temporal redundancy between neighboring frames can be reduced. In MPEG-2, some frames, named interframes, are predicted using a motion estimation based on the conservation of intensity over time. In the new standard MPEG-4, frames are separated into several objects that are transmitted separately. Therefore, the prediction has to be performed on objects instead of frames. So, interframe-objects have to be predicted in order to improve video coding efficiency. The goal of this paper is to propose a new method for object-based prediction using the level sets. First, we propose an efficient object-based motion estimation. The motion of the objects is estimated by assuming the conservation of the level sets function over time, instead of the conservation of the intensity. Secondly, the estimation of the object motion between two frames is used to predict interframe-objects using both forward and backward motion estimations. The method is evaluated on real sequences, illustrating the potential of our approach for an object-based prediction of interframes.