Independent Modes of Variation in Point Distribution Models

Marco Bressan, Jordi Vitrià

Abstract. The main motivation behind this work is to test the feasibility of statistically independent parameters to represent shape variation. This is achieved by using an Independent Component Analysis (ICA) representation as an alternative to Principal Component Analysis (PCA) for the representation of Point Distribution Models. Alongside with this objective, some natural problems arise, and they are also treated in this work. ICA is a general-purpose statistical technique with a wide range of applications in neural computing, signal processing and statistics [41, 17, 8, 14]. The idea is to transform observed random data such that the transformed components are maximally independent from each other. In practice, ICA´s most widely spread version consists in searching a linear non-orthogonal coordinate system in multivariate data determined by second and higher order statistics. The first part of this work is devoted to the presentation of ICA, methods for its estimation, applications and advantages as a feature extraction technique. The problem of density estimation within the ICA representation is also addressed, and general solutions for this problem are introduced. These estimation techniques proved efficient in most of the experiments which were performed. The problem of classification under the ICA representation also confirmed the accuracy of the estimation. Classification was focused from a bayesian perspective and the basic underlying theory is also exposed in this work. A practical example comparing this classification scheme with more classical methods is briefly mentioned.

Key words: Point Distribution Model, Independent Component Analysis, Statistical Model, Independent Modes of Variation, Shape Models, Sparse Coding.

Registration: PIRDI-3/00, November 2000.

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