Local matching of surfaces using a boundary-centered radial decomposition

Abstract

A new surface representation, the “distance profile” is introduced. A distance profile is a decomposition of a surface into “distance contours,” each of which is the locus of all points a certain distance r from a point called the “center point.” The distance contour is in turn represented as a plot of the contour's distance from its centroid as a function of arc length along the contour. The distance profile representation is invariant with respect to rotation about the center point and thus is ideal for “rigid matching” (where the correspondence function between two objects is a rotation and/or translation). For global matching, the center point can be the centroid of the surface. For local matching, we compute multiple distance profiles, each centered around a “critical point” on the surface (a minimum or maximum of curvature or a sharp peak in the surface). This comprises the “boundary-centered radial decomposition.” An implementation of a local surface matcher based on theboundary-centered radial decomposition is described.