A SAEM algorithm for the estimation of template and deformation parameters in medical image sequences |
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Authors: | Frédéric J P Richard Adeline M M Samson Charles A Cuénod |
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Institution: | 1. Department of Mathematics, University Paris Descartes, MAP5, CNRS UMR 8145, Paris, France 2. Hospital Georges Pompidou, Service of Radiology, University Paris Descartes, LRI-EA4062, Paris, France
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Abstract: | 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. |
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