Globally Optimal Interactive Boundary Extraction Using Markov Chain Modeling

Abstract

We present a novel boundary-based (discontinuity tracking) hierarchical statistical criterion to address the interactive contour extraction problem. Our criterion relies on a Markov Chain representation of the boundary and can be efficiently optimized using Dijkstra's algorithm for solving the shortest paths problem. Unlike other criteria optimized with Dijkstra's algorithm, ours is capable of extracting geometrically complex boundaries even when the features incorporated in the objective function are based only on user markings on a small part of the image. The critical quantity in our criterion that yields the above-mentioned results is a normalization factor that boosts the probability of a particular boundary segment based on the candidate boundary segments in its vicinity. Although similar in spirit to the technique of non-maximum suppression routinely employed in edge detection, our method boosts gradually the probability of a particular segment given its surroundings using windows of increasing size in a hierarchical fashion.