Maintaining Valid Topology with Active Contours: Theory and Application

Abstract

We develop and prove correct an algorithm that enables active contours to correctly represent regions that undergo topology changes as the contours evolve. Using the incremental motion typical of active contours, we introduce the concept of motion regions to determine the new topology. When the topology changes (e.g. by contours intersecting), the motion regions are used to delete and and reconnect the contours to accurately describe the new region. Contour intersections can also occur without topology changes. These are also appropriately handled. The algorithm to perform this task is proved correct in a general framework that makes few assumptions about the contour representation. We describe how this algorithm is applied to a polygonal representation of the contours, and argue that it does not significantly affect execution time. Finally, this polygonal implementation is used in surface extraction and phytoplankton classification.