Context, Computation, and Optimal ROC Performance in Hierarchical Models
International Journal of Computer Vision
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This thesis is a mathematical and computational study of compositional vision. Three topics are covered: (1) ROC performance in a compositional world; (2) the construction of a probabilistic model for compositional structure; and (3) the construction of probabilistic model of image gray levels for a given vocabulary of elementary parts.Chapter 1 introduces compositional vision and a probabilistic framework for modeling hierarchy, reusability, and conditional data models.Chapter 2 focuses on theoretical questions about the ROC performance of various approaches to recognition in hypothetical compositional worlds. The results suggest that even sub-optimal decisions within a hierarchical framework will substantially outperform a decision process that does not explicitly allow for part-based decomposition.Chapter 3 focuses on the first component of the Bayesian approach to compositional vision: a prior probability model on hierarchical image interpretations. Non-Markovian (context-sensitive) distributions are investigated, and two theoretical questions are addressed. The existence of a class of non-Markovian distributions is established, and the convergence of an iterative perturbation scheme for achieving these distributions is proven.Chapter 4 focuses on the second component of the Bayesian approach to compositional vision: a probability model on pixel intensities conditioned on a given hierarchical structure. In particular, a generative approach to modeling object parts is developed through a probabilistic extension of the idea of fragment-based templates.Chapter 5 makes some conclusions and suggests future directions.