A Novel Riemannian Framework for Shape Analysis of 3D Objects

In this paper we introduce a novel Riemannian framework for shape analysis of parameterized surfaces. We derive a distance function between any two surfaces that is invariant to rigid motion, global scaling, and reparametrization. It is the last part that presents the main difficulty. Our solution to this problem is twofold: (1) we define a special representation, called a q-map, to represent each surface, and (2) we develop a gradient-based algorithm to optimize over different re-parameterizations of a surface. The second step is akin to deforming the mesh on a fixed surface to optimize its placement. (This is different from the current methods that treat the given meshes as fixed.) Under the chosen representation, with the L2 metric, the action of the re-parametrization group is by isometries. This results in, to our knowledge, the first Riemannian distance between parameterized surfaces to have all the desired invariances. We demonstrate this framework with several examples us...

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Sebastian Kurtek, Eric Klassen, Anuj Srivastava, Zhaohua Ding
• Keywords: Computer Vision, CVPR 2010, Distance Function, Parameterized Surfaces, first Riemannian Distance