Team MISTIS

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Section: New Results

Markov models

Cooperative clustering

Participant : Florence Forbes.

Joint work with:Scherrer, B. and Dojat, M (Grenoble Institute of Neuroscience).

Clustering is a fundamental data analysis step that consists in producing a partionning of the individuals to account for the groups existing in the observed data. In this paper, we introduce an additional cooperative aspect and propose a framework for more general tasks. We address cases in which the goal is to produce not a single partionning but two or more partionnings using cooperation between them. Cooperation is expressed by assuming the existence of two sets of missing assignment variables, representing two sets of labels which are not independent but related in the sense that information on one of them is useful to find the other one. We consider non trivial situations in which Markov random field models are used to deal with additional interactions including dependencies between labels within each label sets. We show that our cooperative setting can be formulated in terms of conditional models and propose then to simplify inference into alternating and cooperative estimation procedures based on variants of the Expectation Maximization (EM) algorithm. We illustrate the advantages of our approach by showing its ability to deal successfully with the complex task of segmenting simultaneously and cooperatively tissues and structures from MRI brain scans. In particular this framework is used in the work described in the next section.

Fully Bayesian Joint Model for MR Brain Scan Tissue and Structure Segmentation

Participant : Florence Forbes.

Joint work with:Scherrer, B., Dojat, M. (Grenoble Institute of Neuroscience) and Garbay, C. (LIG).

Difficulties in automatic MR brain scan segmentation arise from various sources. The nonuniformity of image intensity results in spatial intensity variations within each tissue, which is a major obstacle to an accurate automatic tissue segmentation. The automatic segmentation of subcortical structures is a challenging task as well. It cannot be performed based only on intensity distributions and requires the introduction of a priori knowledge. Most of the proposed approaches share two main characteristics. First, tissue and subcortical structure segmentations are considered as two successive tasks and treated relatively independently although they are clearly linked: a structure is composed of a specific tissue, and knowledge about structures locations provides valuable information about local intensity distribution for a given tissue. Second, tissue models are estimated globally through the entire volume and then suffer from imperfections at a local level. Alternative local procedures exist but are either used as a preprocessing step or use redundant information to ensure consistency of local models. Recently, we reported good results using an innovative local and cooperative approach [54] . It performs tissue and subcortical structure segmentation by distributing through the volume a set of local Markov Random Field (MRF) models which better reflect local intensity distributions. Local MRF models are used alternatively for tissue and structure segmentations. Although satisfying in practice, these tissue and structure MRF's do not correspond to a valid joint probabilistic model and are not compatible in that sense. As a consequence, important issues such as convergence or other theoretical properties of the resulting local procedure cannot be addressed. In addition, in [54] , cooperation mechanisms between local models are somewhat arbitrary and independent of the MRF models themselves. Our contribution [38] is then to propose a fully Bayesian framework in which we define a joint model that links local tissue and structure segmentations but also the model parameters so that both types of cooperations, between tissues and structures and between local models, are deduced from the joint model and optimal in that sense. Our model has the following main features: 1) cooperative segmentation of both tissues and structures is encoded via a joint probabilistic model specified through conditional MRF models which capture the relations between tissues and structures. This model specifications also integrate external a priori knowledge in a natural way; 2) intensity nonuniformity is handled by using a specific parametrization of tissue intensity distributions which induces local estimations on subvolumes of the entire volume; 3) global consistency between local estimations is automatically ensured by using a MRF spatial prior for the intensity distributions parameters. Estimation within our framework is defined as a Maximum A Posteriori (MAP) estimation problem and is carried out by adopting an instance of the Expectation Maximization (EM) algorithm. We show that such a setting can adapt well to our conditional models formulation and simplifies into alternating and cooperative estimation procedures for standard Hidden MRF models. The approach is implemented using a multi-agent framework where each agent computes a local MRF model and cooperates with its neighboring agents for model refinement. The evaluation performed using a previously linearly registered atlas of 17 structures show good results. An illustration is given in FigureĀ  2 .

Figure 2. Real 3T brain scan (a). Images (b) and (c): structure segmentation by our method and corresponding improved tissue segmentation. Image (d): 3-D reconstruction of the 17 segmented structures: the two lateral ventricules, caudates, accumbens, putamens, thalamus, pallidums, hippocampus, amygdalas and the brain stem. The computational time was <15 min after the registration step.
IMG/map199_z121_glIMG/map199_z121_ts_sIMG/map199_z121_ts_tIMG/map199_z121_ts_s3d
(a)(b)(c)(d)

Brain lesions segmentation from multiple MR sequences

Participants : Florence Forbes, Senan Doyle.

Joint work with:Scherrer, B. Dojat, M. (Grenoble Institute of Neuroscience) and Garbay, C. (LIG).

The analysis of MR brain scans is a complex task that is further complicated if the observed data are themselves multi-dimensional as it is the case when several MR channels can provide complementary information and are considered simultaneously. Usually healthy subjects data do not address the same issues as pathological data. This type of data rarely allows the use of automatic or generic approaches. Our goal is to extend our current framework to MRIs with Multiple Sclerosis lesions and stroke lesions. We address the issue of fusing the output of multiple MR sequences to robustly and accurately segment brain lesions. A key capability for radiologists is to delineate lesions out from the rest of the brain tissues. To achieve this goal, radiologists make usually use of multiple MR sequences. The use of multiple sequences not only provides more measurements when segmenting the brain into regions, but crucially, different sequences may be complementary in that one may succeed when another fails. To achieve the same goal automatically and robustly is not an easy task. Overall system performance may be improved in two main ways, either by enhancing the processing of each individual sequence, or by improving the scheme for integrating the information from the different sequences. The contributions of this work concern the latter. We developed a model in which weights can be introduced to account for the relative importance of each modality and propose a variant of the EM algorithm in a Bayesian framework to estimate these weights iteratively and derive a segmentation of the lesions under consideration. Promising results are observed on patients with Multiple Sclerosis lesions (see Figure 3 ).

Figure 3. Segmentation of MS lesions from 3 MR images. Our weighted EM procedure (last column) is able to recover a large part of the lesions starting from an initial poor selected ROI (first column). The second and third columns show that weighting is important and must be done adaptively.
IMG/wem

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