Statistical shape analysis using kernel PCA

Mercer kernels are used for a wide range of image and signal processing tasks like de-noising, clustering, discriminant analysis etc. These algorithms construct their solutions in terms of the expansions in a high-dimensional feature space F. However, many applications like kernel PCA (principal component analysis) can be used more effectively if a pre-image of the projection in the feature space is available. In this paper, we propose a novel method to reconstruct a unique approximate pre-image of a feature vector and apply it for statistical shape analysis. We provide some experimental results to demonstrate the advantages of kernel PCA over linear PCA for shape learning, which include, but are not limited to, ability to learn and distinguish multiple geometries of shapes and robustness to occlusions.

[1]  W. Eric L. Grimson,et al.  A shape-based approach to the segmentation of medical imagery using level sets , 2003, IEEE Transactions on Medical Imaging.

[2]  Olivier D. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[3]  Gunnar Rätsch,et al.  Kernel PCA and De-Noising in Feature Spaces , 1998, NIPS.

[4]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[5]  Ivor W. Tsang,et al.  The pre-image problem in kernel methods , 2003, IEEE Transactions on Neural Networks.

[6]  Bernhard Schölkopf,et al.  The Kernel Trick for Distances , 2000, NIPS.

[7]  Szymon Rusinkiewicz,et al.  Modeling by example , 2004, ACM Trans. Graph..

[8]  Gunnar Rätsch,et al.  Invariant Feature Extraction and Classification in Kernel Spaces , 1999, NIPS.

[9]  Tony F. Chan,et al.  Level set based shape prior segmentation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).