Intrinsic girth function for shape processing

Abstract

We introduce the intrinsic girth function (IGF), a scalar field on a manifold closed surface. For each point p on the surface, the value of the IGF at p is the length of the globally shortest geodesic path starting from and ending at p. Therefore, th IGF is defined intrinsically and captures geometric properties more globally than surface curvature but more locally than the geodesic centricity and eccentricity functions. The IGF is invariant under isometry, insensitive to mesh tessellations, and robust to geometric noises and local surface variations. We shall present the applications of the IGF to shape retrieval and identifying tip parts and tube/plate structures of 3D shapes. Computationally, we develop an efficient method for computing the IGF with an empirical complexity of O(n2 log n) time and O(n) space, where n is the number of vertices of a triangle mesh surface representing the input shape.