Chapter

Geometric Science of Information

Volume 8085 of the series Lecture Notes in Computer Science pp 120-127

Random Spatial Structure of Geometric Deformations and Bayesian Nonparametrics

  • Christof SeilerAffiliated withDepartment of Statistics, Stanford University
  • , Xavier PennecAffiliated withAsclepios Project, INRIA Sophia Antipolis
  • , Susan HolmesAffiliated withDepartment of Statistics, Stanford University

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Abstract

Our work is motivated by the geometric study of lower back pain from patient CT images. In this paper, we take a first step towards that goal by introducing a data-driven way of identifying anatomical regions of interest. We propose a probabilistic model of the geometrical variability and describe individual patients as noisy deformations of a random spatial structure (modeled as regions) from a common template. The random regions are generated using the distance dependent Chinese Restaurant Process. We employ the Gibbs sampler to infer regions from a set of noisy deformation fields. Each step of the sampler involves model selection (Bayes factor) to decide about fusing regions. In the discussion, we highlight connections between image registration and Markov chain Monte Carlo methods.