Bayesian mixed effect atlas estimation with a diffeomorphic deformation model

Stéphanie Allassonnière (1) , Stanley Durrleman (2, 3) , Estelle Kuhn (4)

1 X - École polytechnique
2 ICM - Institut du Cerveau = Paris Brain Institute
3 ARAMIS - Algorithms, models and methods for images and signals of the human brain = Algorithmes, modèles et méthodes pour les images et les signaux du cerveau humain [ICM Paris]
4 MIA-JOUY - Unité de biométrie et intelligence artificielle de Jouy

In this paper we introduce a diffeomorphic constraint on the deformations considered in the deformable Bayesian Mixed Effect (BME) Template model. Our approach is built on a generic group of diffeomorphisms, which is parametrized by an arbitrary set of control point positions and momentum vectors. This enables to estimate the optimal positions of control points together with a template image and parameters of the deformation distribution which compose the atlas. We propose to use a stochastic version of the Expectation-Maximization (EM) algorithm where the simulation is performed using the Anisotropic Metropolis Adjusted Langevin Algorithm (AMALA). We propose also an extension of the model including a sparsity constraint to select an optimal number of control points with relevant positions. Experiments are carried out on the USPS database and on mandibles of mice.

Keywords: deformable template model; atlas estimation; stochastic algorithm; control point optimization; sparsity; diffeomorphic deformations

Keywords: Anisotropic MALA

Domains: Mathematics [math]; Computer Science [cs]

Stéphanie Allassonnière, Stanley Durrleman, Estelle Kuhn. Bayesian mixed effect atlas estimation with a diffeomorphic deformation model. [Technical Report] R2014-2, Inra. 2014. ⟨hal-02801668⟩