Optimal designs for three-dimensional shape analysis with spherical harmonic descriptors

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dc.creatorDette, Holger
dc.creatorMelas, Viatcheslav B.
dc.creatorPepelyshev, Andrey
dc.date2006-03-03
dc.date.accessioned2026-07-07T08:07:37Z
dc.date.available2026-07-07T08:07:37Z
dc.descriptionWe determine optimal designs for some regression models which are frequently used for describing three-dimensional 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 $Φ_p$ criteria proposed by Kiefer in 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 three-dimensional shape analysis.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053605000000552 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0603075
dc.identifierhttp://arxiv.org/abs/math/0603075
dc.identifierAnnals of Statistics 2005, Vol. 33, No. 6, 2758-2788
dc.identifierdoi:10.1214/009053605000000552
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130993
dc.subjectStatistics Theory
dc.subject62K05, 65D32 (Primary)
dc.titleOptimal designs for three-dimensional shape analysis with spherical harmonic descriptors
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