Robust designs for 3D shape analysis with spherical harmonic descriptors

dc.contributor.authorDette, Holger
dc.contributor.authorWiens, Douglas P.
dc.date.accessioned2007-05-25T11:58:29Z
dc.date.available2007-05-25T11:58:29Z
dc.date.issued2007-05-25T11:58:29Z
dc.description.abstractSpherical harmonic descriptors are frequently used for describing three-dimensional shapes in terms of Fourier coefficients corresponding to an expansion of a function defined on the unit sphere. In a recent paper Dette, Melas and Pepelysheff (2005) determined optimal designs with respect to Kiefer's Phi p-criteria for regression models derived from a truncated Fourier series. In particular it was shown that the uniform distribution on the sphere is Phi p-optimal for spherical harmonic descriptors, for all p > -1. These designs minimize a function of the variance-covariance matrix of the least squares estimate but do not take into account the bias resulting from the truncation of the series. In the present paper we demonstrate that the uniform distribution is also optimal with respect to a minimax criterion based on the mean square error, and as a consequence these designs are robust with respect to the truncation error. Moreover, we also consider heteroscedasticity and possible correlations in the construction of the optimal designs. These features appear naturally in 3D shape analysis, and the uniform design again turns out to be minimax robust against erroneous assumptions of homoscedasticity and independence. AMS 2000 Subject Classi cation: Primary 62K05, 62D32; secondary 62J05.en
dc.identifier.urihttp://hdl.handle.net/2003/24313
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-284
dc.language.isoende
dc.subject3D-image dataen
dc.subjectDependent dataen
dc.subjectMean square erroren
dc.subjectMinimax optimal designsen
dc.subjectOptimal designsen
dc.subjectRobust designsen
dc.subjectShape analysisen
dc.subjectSpherical harmonic descriptorsen
dc.subject.ddc004
dc.titleRobust designs for 3D shape analysis with spherical harmonic descriptorsen
dc.typeTextde
dc.type.publicationtypereporten
dcterms.accessRightsopen access

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