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Polynomial Eulerian Shape Distributions

dc.contributor.authorCaro-Lopera F.J.; Díaz-García J.A.
dc.date.accessioned2025-04-28T22:09:10Z
dc.date.available2025-04-28T22:09:10Z
dc.date.created2024
dc.identifier.issn10665307
dc.identifier.urihttp://hdl.handle.net/11407/8802
dc.descriptionAbstract: In this paper a new approach is derived in the context of shape analysis. The so called polynomial Eulerian shape theory solves an open problem proposed in [27] about the construction of certain shape density involving Euler hypergeometric functions of matrix arguments. The associated distribution is obtained by a connection between the required shape invariants and a known result on canonical correlations published in 1963. As usual in matrix variate statistical shape theory, the densities are expressed in terms of infinite series of zonal polynomials. However, if we consider certain parametric subspace for the parity of the number of landmarks, the computational problem can be solved analytically by deriving the Eulerian matrix relation of two matrix arguments. Under that restriction, the analysis of classical landmark data is based on polynomial distribution with small degree. Finally, a methodology to compare Eulerian shape and landmark discrimination under equivalent classes is proposed and applied in machine vision. © Allerton Press, Inc. 2024.
dc.language.isoeng
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85217388182&doi=10.3103%2fS1066530724700194&partnerID=40&md5=9cfdf83aa4b8839ec0433203acae9460
dc.sourceMathematical Methods of Statistics
dc.sourceMath. Methods Stat.
dc.sourceScopus
dc.subjectCorrelation structure
dc.subjectEuler matrix relation
dc.subjectPolynomial distributions
dc.subjectShape theory
dc.subjectZonal polynomials
dc.subjectCorrelation structure
dc.subjectEuler matrix relation
dc.subjectPolynomial distributions
dc.subjectShape theory
dc.subjectZonal polynomials
dc.titlePolynomial Eulerian Shape Distributions
dc.typeArticle
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.type.spaArtículo revisado por pares
dc.identifier.doi10.3103/S1066530724700194
dc.relation.citationvolume33
dc.relation.citationissue4
dc.relation.citationstartpage373
dc.relation.citationendpage391
dc.publisher.facultyFacultad de Ciencias Básicas
dc.affiliationCaro-Lopera F.J., University of Medellin, Faculty of Basic Sciences, Medellín, Colombia
dc.affiliationDíaz-García J.A., Universidad Autónoma de Chihuahua, Facultad de Zootecnia y Ecología, Chihuahua, Mexico
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dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellín
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.instnameinstname:Universidad de Medellín


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