We have developed an integrated approach to modeling, extracting, detecting and classifying deformable contours directly from noisy images. We have conducted a case study on regularization, formulation and initialization of active contour models (snakes). Using the minimax principle, we derived a regularization criterion whereby the values can be automatically and implicitly determined along the contour. Furthermore, we formulated a set of energy functionals which yield snakes that contain Hough transform as a special case. Subsequently, we considered the problem of modeling and extracting arbitrary deformable contours from noisy images. We combined a stable, invariant and unique contour model with Markov random fields 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 integrated these lower-level visual tasks with pattern recognition processes of detection and classification. Based on the Nearman-Pearson lemma, we derived 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 has been confirmed by extensive and rigorous experimentation.
GSNAKE software is available