A Part‐aware Surface Metric for Shape Analysis

The notion of parts in a shape plays an important role in many geometry problems, including segmentation, correspondence, recognition, editing, and animation. As the fundamental geometric representation of 3D objects in computer graphics is surface‐based, solutions of many such problems utilize a surface metric, a distance function defined over pairs of points on the surface, to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts: shape parts and surface metric. Specifically, we develop a surface metric that is part‐aware. To encode part information at a point on a shape, we model its volumetric context – called the volumetric shape image (VSI) – inside the shape's enclosed volume, to capture relevant visibility information. We then define the part‐aware metric by combining an appropriate VSI distance with geodesic distance and normal variation. We show how the volumetric view on part separation addresses certain limitations of the surface view, which relies on concavity measures over a surface as implied by the well‐known minima rule. We demonstrate how the new metric can be effectively utilized in various applications including mesh segmentation, shape registration, part‐aware sampling and shape retrieval.