Medial Meshes for Volume Approximation

Abstract: Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple primitives. In this study, we propose a new volume representation, called medial meshes, and present an efficient method for its computation. Specifically, we use the union of a novel type of simple volume primitives, which are spheres and the convex hulls of two or three spheres, to approximate a given 3D shape. We compute such a volume approximation based on a new method for medial axis simplification guided by Hausdorff errors. We further demonstrate the superior efficiency and accuracy of our method over existing methods for medial axis simplification.