Stéphanie Allassonnière

Geodesic shooting and diffeomorphic matching via textured meshes

We propose a new approach in the context of diffeomorphic image matching with free boundaries. A region of interest is triangulated over a template, which is considered as a grey level textured mesh. A diffeomorphic transformation is then approximated by the piecewise affine deformation driven by the displacements of the vertices of the triangles. This provides a finite dimensional, landmark-type, reduction for this dense image comparison problem. Based on an optimal control model, we analyze and compare two optimization methods formulated in terms of the initial momentum: direct optimization by gradient descent, or root-finding for the transversality equation, enhanced by a preconditioning of the Jacobian. We finally provide a series of numerical experiments on digit and face matching.

A stochastic algorithm for probabilistic independent component analysis

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic approximation of the standard EM algorithm. We demonstrate the applicability of the method on a large range of decomposition models and illustrate the developments with experimental results on various data sets.

Bayesian Mixed Effect Atlas Estimation with a Diffeomorphic Deformation Model

In this paper we introduce a diffeomorphic constraint on the deformations considered in the deformable Bayesian mixed effect template model. Our approach is built on a generic group of diffeomorphisms, which is parameterized by an arbitrary set of control point positions and momentum vectors. This enables us 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 algorithm where the simulation is performed using the anisotropic Metropolis adjusted Langevin algorithm. 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 United States Postal Service database, on mandibles of mice, and on three-dimensional murine dendrite spine images.

Inconsistency of template estimation by minimizing of the variance/pre-variance in the quotient space

We tackle the problem of template estimation when data have been randomly deformed under a group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Fr{e}chet mean in the quotient space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In the first part, we restrict ourselves to isometric group action, in this case the Hilbertian distance is invariant under the group action. We establish an asymptotic behavior of the consistency bias which is linear with respect to the noise level. As a result the inconsistency is unavoidable as soon as the noise is enough. In practice, template estimation with a finite sample is often done with an algorithm called max-max. In the second part, also in the case of isometric group finite, we show the convergence of this algorithm to an empirical Karcher mean. Our numerical experiments show that the bias observed in practice can not be attributed to the small sample size or to a convergence problem but is indeed due to the previously studied inconsistency. In a third part, we also present some insights of the case of a non invariant distance with respect to the group action. We will see that the inconsistency still holds as soon as the noise level is large enough. Moreover we prove the inconsistency even when a regularization term is added.

Spatiotemporal Propagation of the Cortical Atrophy: Population and Individual Patterns

Repeated failures in clinical trials for Alzheimer’s disease (AD) have raised a strong interest for the prodromal phase of the disease. A better understanding of the brain alterations during this early phase is crucial to diagnose patients sooner, to estimate an accurate disease stage, and to give a reliable prognosis. According to recent evidence, structural alterations in the brain are likely to be sensitive markers of the disease progression. Neuronal loss translates in specific spatiotemporal patterns of cortical atrophy, starting in the enthorinal cortex and spreading over other cortical regions according to specific propagation pathways. We developed a digital model of the cortical atrophy in the left hemisphere from prodromal to diseased phases, which is built on the temporal alignment and combination of several short-term observation data to reconstruct the long-term history of the disease. The model not only provides a description of the spatiotemporal patterns of cortical atrophy at the group level but also shows the variability of these patterns at the individual level in terms of difference in propagation pathways, speed of propagation, and age at propagation onset. Longitudinal MRI datasets of patients with mild cognitive impairments who converted to AD are used to reconstruct the cortical atrophy propagation across all disease stages. Each observation is considered as a signal spatially distributed on a network, such as the cortical mesh, each cortex location being associated to a node. We consider how the temporal profile of the signal varies across the network nodes. We introduce a statistical mixed-effect model to describe the evolution of the cortex alterations. To ensure a spatiotemporal smooth propagation of the alterations, we introduce a constrain on the propagation signal in the model such that neighboring nodes have similar profiles of the signal changes. Our generative model enables the reconstruction of personalized patterns of the neurodegenerative spread, providing a way to estimate disease progression stages and predict the age at which the disease will be diagnosed. The model shows that, for instance, APOE carriers have a significantly higher pace of cortical atrophy but not earlier atrophy onset.