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This paper proposes a novel framework for multi-group shape analysis relyingon a hierarchical graphical statistical model on shapes within a population.Theframework represents individual shapes as point setsmodulo translation,rotation, and scale, following the notion in Kendall shape space.Whileindividual shapes are derived from their group shape model, each group shapemodel is derived from a single population shape model. The hierarchical modelfollows the natural organization of population data and the top level in thehierarchy provides a common frame of reference for multigroup shape analysis,e.g. classification and hypothesis testing. Unlike typical shape-modelingapproaches, the proposed model is a generative model that defines a jointdistribution of object-boundary data and the shape-model variables.Furthermore, it naturally enforces optimal correspondences during the processof model fitting and thereby subsumes the so-called correspondence problem. Theproposed inference scheme employs an expectation maximization (EM) algorithmthat treats the individual and group shape variables as hidden random variablesand integrates them out before estimating the parameters (population mean andvariance and the group variances). The underpinning of the EM algorithm is thesampling of pointsets, in Kendall shape space, from their posteriordistribution, for which we exploit a highly-efficient scheme based onHamiltonian Monte Carlo simulation. Experiments in this paper use the fittedhierarchical model to perform (1) hypothesis testing for comparison betweenpairs of groups using permutation testing and (2) classification for imageretrieval. The paper validates the proposed framework on simulated data anddemonstrates results on real data.

Hierarchical Graphical Models for Multigroup Shape Analysis using Expectation Maximization with Sampling in Kendall's Shape Space