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 generalpurpose 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 nonorthogonal 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: PIRDI3/00, November 2000.

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