Template estimation form unlabeled point set data and surfaces for Computational Anatomy

Abstract : A central notion in Computational Anatomy is the generation of registration maps,mapping a large set of anatomical data to a common coordinate system to study intra-population variability and inter-population differences. In previous work methods for estimating the common coordinate system or the template given a collection imaging data were presented based on the notion of Frechet mean estimation using a metric on the space of diffeomorphisms. In this paper we extend the methodology to the estimation of a template given a collection of unlabeled point sets and surfaces. Using a representation of points and surfaces as currents a Reproducing Kernel Hilbert Space (RKHS) norm is induced on the space of Borel measures. Using this norm and a metric on the space of diffeomorphisms the template estimation problem is possed as a minimum mean squared error estimation problem. An efficient alternating conjugate gradient decent algorithm is derived and results exemplifying the methodology are presented.
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Joan Alexis Glaunès, Sarang Joshi. Template estimation form unlabeled point set data and surfaces for Computational Anatomy. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. ⟨hal-00263576⟩

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