Authors: Dette, Holger
Melas, Viatcheslav B.
Pepelyshev, Andrey
Title: Optimal designs for 3D shape analysis with spherical harmonic descriptors
Language (ISO): en
Abstract: We determine optimal designs for some regression models which are frequently used for describing 3D shapes. These models are based on a Fourier expansion of a function defined on the unit sphere in terms of spherical harmonic basis functions. In particular it is demonstrated that the uniform distribution on the sphere is optimal with respect to all Φp-criteria proposed by Kiefer (1974) and also optimal with respect to a criterion which maximizes a p-mean of the r smallest eigenvalues of the variance-covariance matrix. This criterion is related to principal component analysis, which is the common tool for analyzing this type of image data. Moreover, discrete designs on the sphere are derived, which yield the same information matrix in the spherical harmonic regression model as the uniform distribution and are therefore directly implementable in practice. It is demonstrated that the new designs are substantially more efficient than the commonly used designs in 3D-shape analysis.
Subject Headings: shape analysis
spherical harmonic descriptors
optimal designs
quadrature formulas
principal component analysis
3D-image data
Issue Date: 2004
Provenance: Universitätsbibliothek Dortmund
Appears in Collections:Sonderforschungsbereich (SFB) 475

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