Total Bregman divergence and its applications to shape retrieval

Shape database search is ubiquitous in the world of biometric systems, CAD systems etc. Shape data in these domains is experiencing an explosive growth and usually requires search of whole shape databases to retrieve the best matches with accuracy and efficiency for a variety of tasks. In this paper, we present a novel divergence measure between any two given points in Rn or two distribution functions. This divergence measures the orthogonal distance between the tangent to the convex function (used in the definition of the divergence) at one of its input arguments and its second argument. This is in contrast to the ordinate distance taken in the usual definition of the Bregman class of divergences [4]. We use this orthogonal distance to redefine the Bregman class of divergences and develop a new theory for estimating the center of a set of vectors as well as probability distribution functions. The new class of divergences are dubbed the total Bregman divergence (TBD). We present th...

• Type: Conference
• Year: 2010
• Where: CVPR
• Authors: Meizhu Liu, Baba C. Vemuri, Shun-ichi Amari, Frank Nielsen
• Keywords: Computer Vision, CVPR 2010, Divergence, Orthogonal Distance, Shape Databases