A Novel Riemannian Framework for Shape Analysis of 3D Objects
published: July 19, 2010, recorded: June 2010, views: 5252
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
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 using some toy shapes, and real data with anatomical structures, and cropped facial surfaces. We also successfully demonstrate clustering and classification of these objects under the proposed metric.
Download slides: cvpr2010_kurtek_nrfs_01-1.pdf (3.8 MB)
Download slides: cvpr2010_kurtek_nrfs_01.ppt (5.3 MB)
Download article: cvpr2010_kurtek_nrfs_01.pdf (1.8 MB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !