Introducing a crystalline flow for a contour figure analysis

We introduce a crystalline flow for a contour figure analysis. The crystalline flow is a special family of evolving polygons, and is considered as a discrete version of a classical curvature flow. In the evolving process of the crystalline flow, each facet moves toward its normal direction. The velocity of the facet is determined by the nonlocal curvature, which depends on the length of the facet. Different from a classical curvature flow, it is easy to track each facet in a given contour through the evolving process, because a given polygon remains polygonal. This aspect helps us to make a scale-space representation of a contour in an image. In this article, we present a method for extracting dominant corners using a crystalline flow. Experimental results show that our method extracts several sets of dominant corner facets successfully from a given contour figure.