17 February 2006 Statistical shape analysis using kernel PCA
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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.
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Yogesh Rathi, Yogesh Rathi, Samuel Dambreville, Samuel Dambreville, Allen Tannenbaum, Allen Tannenbaum, } "Statistical shape analysis using kernel PCA", Proc. SPIE 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, 60641B (17 February 2006); doi: 10.1117/12.641417; https://doi.org/10.1117/12.641417

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