Abstract
Grenander & Miller (1994) describe a model for representing amorphous two-dimensional objects with no obvious landmark. Each object is represented by n vertices around its perimeter, and is described by deforming an n-sided regular polygon using edge transformations. A multivariate normal distribution with a block circulant covariance matrix is used to model these edge transformations. The purpose of this paper is to describe in detail the statistical properties of this multivariate model and the eigenstructure of the covariance matrix. Various special cases of the model are considered, including articulated models and conditional Markov random field models. We consider maximum likelihood based inference and the model is applied to some datasets to explore shape variability.
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