Using circulant symmetry to model featureless objects

• 成果类型: Article
• 署名作者: Kent, JT; Dryden, IL; Anderson, CR
• 署名单位: University of Leeds; University of Nottingham
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/87.3.527
• 发表日期: 2000
• 页码: 527544
• 关键词: particles; shape

摘要

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.