Enforcing local context into shape statistics

Hong, Byung-Woo
Soatto, Stefano
Vese, Luminita A.

¹School of Computer Science and Engineering, Chung-Ang University, Seoul, Korea; e-mail: [email protected]
²Computer Science Department, University of California, Los Angeles, CA, USA; e-mail: [email protected]
³Department of Mathematics, University of California, Los Angeles, CA, USA; e-mail: [email protected]

Communicated by Lixin Shen and Yuesheng Xu.

For any questions regarding this manuscript, please contact the corresponding author Byung-Woo Hong.

Received: 23 October 2007; Accepted: 1 October 2008

Advances in Computational Mathematics 31(3):p 185-213, October 2009.

The paper presents a variational framework to compute first and second order statistics of an ensemble of shapes undergoing deformations. Geometrically “meaningful” correspondence between shapes is established via a kernel descriptor that characterizes local shape properties. Such a descriptor allows retaining geometric features such as high-curvature structures in the average shape, unlike conventional methods where the average shape is usually smoothed out by generic regularization terms. The obtained shape statistics are integrated into segmentation as a prior knowledge. The effectiveness of the method is demonstrated through experimental results with synthetic and real images.