Deformable Contours: Modeling, Extraction, Detection and Classification
K. F. Lai, Ph.D. Dissertation, Electrical and Computer Engineering Department, August 1994.

Abstract

This thesis presents an integrated approach in modeling, extracting, detecting and classifying deformable contours directly from noisy images. We begin by conducting a case study on regularization, formulation and initialization of the active contour models (snakes). Using minimax principle, we derive a regularization criterion whereby the values can be automatically and implicitly determined along the contour. Furthermore, we formulate a set of energy functionals which yield snakes that contain Hough transform as a special case. Subsequently, we consider the problem of modeling and extracting arbitrary deformable contours from noisy images. We combine a stable, invariant and unique contour model with Markov random field to yield prior distribution that exerts influence over an arbitrary global model while allowing for deformation. Under the Bayesian framework, contour extraction turns into posterior estimation, which is in turn equivalent to energy minimization in a generalized active contour model. Finally, we integrate these lower level visual tasks with pattern recognition processes of detection and classification. Based on the Nearman-Pearson lemma, we derive the optimal detection and classification tests. As the summation is peaked in most practical applications, only small regions need to be considered in marginalizing the distribution. The validity of our formulation have been confirmed by extensive and rigorous experimentations.