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Principal Component Analysis and Laplacian Splines: Steps Toward a Unified Model

Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)

Abstract

Principal component analysis models are widely used to model shapes in medical image analysis, computer vision, and other fields. The “Laplacian” spline approaches including thin-plate splines are also used for this purpose. These alternative approaches have complementary advantages and weaknesses: a low-rank principal component analysis model has some “knowledge” of the data being modeled, but cannot exactly fit arbitrary data, whereas spline models can fit arbitrary data but have only a generic smoothness assumption about the character of the data. In this contribution we show that the data fitting problem for these two approaches can be put into a common form, by making use of a relation between the data covariance and the Laplacian. This suggests the possibility of a unified approach that combines the advantages of each.

Keywords

Principal component analysis Covariance Polyharmonic splines Image registration and tracking 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Victoria University School of Engineering and Computer ScienceWellingtonNew Zealand

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