Polygonal Approximation of Point Sets

Our domain of interest is polygonal (and polyhedral) approximation of point sets. Neither the order of data points nor the number of needed line segments (surface patches) are known. In particular, point sets can be obtained by laser range scanner mounted on a moving robot or given as edge pixels/voxels in digital images. Polygonal approximation of edge pixels can also be interpreted as grouping of edge pixels to parts of object contours. The presented approach is described in the statistical framework of Expectation Maximization (EM) and in cognitively motivated geometric framework. We use local support estimation motivated by human visual perception to evaluate support in data points of EM components after each EM step. Consequently, we are able to recognize a locally optimal solution that is not globally optimal, and modify the number of model components and their parameters. We will show experimentally that the proposed approach has much stronger global convergence properties than the EM approach. In particular, the proposed approach is able to converge to a globally optimal solution independent of the initial number of model components and their initial parameters.