Globally Optimal Grouping for Symmetric Boundaries

Many natural and man-made structures have a boundary that shows certain level of bilateral symmetry, a property that has been used to solve many computer-vision tasks. In this paper, we present a new grouping method for detecting closed boundaries with symmetry. We first construct a new type of grouping token in the form of a symmetric trapezoid, with which we can flexibly incorporate various boundary and region information into a unified grouping cost function. Particularly, this grouping cost function integrates Gestalt laws of proximity, closure, and continuity, besides the desirable boundary symmetry. We then develop a graph algorithm to find the boundary that minimizes this grouping cost function in a globally optimal fashion. Finally, we test this method by some experiments on a set of natural and medical images.