Title

Nonparametric Density Estimation on Homogeneous Spaces in High Level Image Analysis.

Abstract

Thelandmarkdatareductionapproachinhighlevelimageanalysishasledtosignificantprogresstoscenerecognitionviastatisticalshapeanalysis(DrydenandMardia,1998).Whileanumberoffamiliesofsimilarityshapedensitieshaveprovenusefulindataanalysis,onlyafewpara-metricmodelshavebeenconsideredonlyrecentlyinthecontextofprojectiveshape(MardiaandPatrangenaru,2004),oraffineshape.Shapespacesofinteresthavethegeometricstructureofsymmetricspaces:planarsimilarityshapespacesarecomplexprojectivespaces(Kendall,1984),affineshapespacesarerealGrassmannmanifolds(Sparr,1992),andspacesofplanarprojectiveshapesofconfigurationsofpointsingeneralpositionareproductsofrealprojectivespaces(MardiaandPatrangenaru,2004).Therefore,datadrivendensityestimationofshapes,regardedaspointsonsymmetricspacesandarisingfromdigitizinglandmarksinimages,isnecessary.Recently,Pelletier(2004)consideredkerneldensityestimationon"general”Rie-mannianmanifolds;hisresultshoweverholdonlyinhomogeneousspaces.Thisissufficientforimageanalysis,sinceanysymmetricspaceishomogeneous.PelletierestimatorsgeneralizethedensityestimatorsoncertainhomogeneousspacesintroducedbyRuymgaart(1989),byH.Hendriks,J.H.M.JanssenandRuymgaart(1993),andbyLeeandRuymgaart(1998).Inthispaper,weproposeaclassofadjustedPelletierdensityestimators,onhomogeneousspaces,thatconvergeuniformlyandalmostsurelyatthesamerateasnaivekerneldensityestimatorsonEuclideanspaces

Department(s)

Mathematics and Statistics

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2004 Texas Tech University, All rights reserved.

This document is currently not available here.


Share

 
COinS