Quasi-Regularity Verification For 2D Polygonal Objects Based On Medial Axis Analysis

Quasi-regularity has been proved to be a sufficient condition for simple-connectedness preservation during the digitization process of 2D continuous objects. The original definition of quasi-regularity relies on set-based morphological operations of erosion and dilation. With this definition, quasi-regularity is algorithmically difficult to assess. In this paper, we propose a tractable framework for quasi-regularity verification, especially designed for polygons. Our approach mainly relies on the computation and analysis of the medial axis of these objects, and determines their potential quasi-regularity, and thus their ability to undergo a digitization without alteration of their topological properties. The framework is applied in the context of topology-preserving rigid motions of digital objects.