A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Algorithms for Low-Level Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
A simulated annealing version of the EM algorithm for non-Gaussian deconvolution
Statistics and Computing
Optimizing random scan Gibbs samplers
Journal of Multivariate Analysis
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This paper is about object deformations observed throughout a sequence of images. We present a statistical framework in which the observed images are defined as noisy realizations of a randomly deformed template image. In this framework, we focus on the problem of the estimation of parameters related to the template and deformations. Our main motivation is the construction of estimation framework and algorithm which can be applied to short sequences of complex and highly-dimensional images. The originality of our approach lies in the representations of the template and deformations, which are defined on a common triangulated domain, adapted to the geometry of the observed images. In this way, we have joint representations of the template and deformations which are compact and parsimonious. Using such representations, we are able to drastically reduce the number of parameters in the model. Besides, we adapt to our framework the Stochastic Approximation EM algorithm combined with a Markov Chain Monte Carlo procedure which was proposed in 2004 by Kuhn and Lavielle. Our implementation of this algorithm takes advantage of some properties which are specific to our framework. More precisely, we use the Markovian properties of deformations to build an efficient simulation strategy based on a Metropolis-Hasting-Within-Gibbs sampler. Finally, we present some experiments on sequences of medical images and synthetic data.