Stochastic Algorithm For Parameter Estimation For Dense Deformable Template Mixture Model

Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random variable has been given by Allassonni\`ere, Amit and Trouv\'e in [1] in simple and mixture of deformable template models. A consistent stochastic algorithm has been introduced in [2] to face the problem encountered in [1] for the convergence of the estimation algorithm for the one component model in the presence of noise. We propose here to go on in this direction of using some "SAEM-like" algorithm to approximate the MAP estimator in the general Bayesian setting of mixture of deformable template model. We also prove the convergence of this algorithm toward a critical point of the penalised likelihood of the observations and illustrate this with handwritten digit images

Construction of Bayesian Deformable Models via Stochastic Approximation Algorithm: A Convergence Study

The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is especially true in shape modelling in the computer vision community or in probabilistic atlas building for Computational Anatomy (CA). A first coherent statistical framework modelling the geometrical variability as hidden variables has been given by Allassonni\`ere, Amit and Trouv\'e (JRSS 2006). Setting the problem in a Bayesian context they proved the consistency of the MAP estimator and provided a simple iterative deterministic algorithm with an EM flavour leading to some reasonable approximations of the MAP estimator under low noise conditions. In this paper we present a stochastic algorithm for approximating the MAP estimator in the spirit of the SAEM algorithm. We prove its convergence to a critical point of the observed likelihood with an illustration on images of handwritten digits

Detecting Long Distance Conditional Correlations Between Anatomical Regions Using Gaussian Graphical Models

International audienceThe conditional correlation patterns of an anatomical shape may provide some important information on the structure of this shape. We propose to investigate these patterns by Gaussian Graphical Modelling. We design a model which takes into account both local and long-distance dependencies. We provide an algorithm which estimates sparse long-distance conditional correlations, highlighting the most significant ones. The selection procedure is based on a criterion which quantifies the quality of the conditional correlation graph in terms of prediction. The preliminary results on AD versus control population show noticeable differences

Estimating the Template in the Total Space with the Fréchet Mean on Quotient Spaces may have a Bias: a Case Study on Vector Spaces Quotiented by the Group of Translations

International audienceWhen we have a deformation group acting on a vector space of observations, these data are not anymore elements of our space but rather orbits for the group action we consider. If the data are generated from an unknown template with noise, to estimate this template, one may want to minimize the variance in the quotient set. In this article we study statistics on a particular quotient space. We prove that the expected value of a random variable in our vector space mapped in the quotient space is different from the Fréchet mean in the quotient space when the observations are noisy

Bayesian Estimation of Probabilistic Atlas for Anatomically-Informed Functional MRI Group Analyses

International audienceTraditional analyses of Functional Magnetic Resonance Imaging (fMRI) use little anatomical information. The registration of the images to a template is based on the individual anatomy and ignores functional information; subsequently detected activations are not confined to gray matter (GM). In this paper, we propose a statistical model to estimate a probabilistic atlas from functional and T1 MRIs that summarizes both anatomical and functional information and the geometric variability of the population. Registration and Segmentation are performed jointly along the atlas estimation and the functional activity is constrained to the GM, increasing the accuracy of the atlas

Sparse Adaptive Parameterization of Variability in Image Ensembles

International audienceThis paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles. Dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a Hamiltonian flow of self-interacting particles. The proposed approach estimates a template image representative of a given image set, an optimal set of control points that focuses on the most variable parts of the image, and template-to-image registrations that quantify the variability within the image set. The method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain. The optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent. The selection of the control points is done by adding a L 1 prior to the objective function, which is optimized using the FISTA algorithm

MAP Estimation of Statistical Deformable Templates Via Nonlinear Mixed Effects Models : Deterministic and Stochastic Approaches

International audienceIn [1], a new coherent statistical framework for estimating statistical deformable templates relevant to computational anatomy (CA) has been proposed. This paper addresses the problem of population av- erage and estimation of the underlying geometrical variability as a MAP computation problem for which deterministic and stochastic approxima- tion schemes have been proposed. We illustrate some of the numerical issues with handwritten digit and 2D medical images and apply the es- timated models to classification through maximum likelihood