School of ComputingSCI InstituteSpherical Harmonic FunctionAdvanced Image ProcessingXiaoyue HuangSlides from Dr.Guido GerigSchool of ComputingSCI InstituteIntroduction• 3D extension to the 2D case. (pros, cons? ) eg. Hand, fist• Can not simply use chain code as 2D case, why?• Project all the vertexes to a unit ball, why? (no necessary in 2D)• Normalize the area (similar to 2D case, )School of ComputingSCI InstituteThe surface data structureSchool of ComputingSCI InstituteParameterization of closed surface• Starting point– North pole: lower left– South pole: upper right• Assign latitude and longitudeSchool of ComputingSCI InstituteOptimization• Newton-LagrangeSchool of ComputingSCI InstituteParameterization by spherical harmonics basis functionsSchool of ComputingSCI InstituteParameterization by spherical harmonics basis functionsSchool of ComputingSCI InstituteSchool of ComputingSCI InstituteInvariant descriptors• Rotation independent descriptorsSchool of ComputingSCI InstituteInvariant descriptorsSchool of ComputingSCI InstituteParameterization with spherical harmonics• Surface Parameterization & Expansion into spherical harmonics.• Normalization of surface mesh (alignment to first ellipsoid).• Correspondence: Homology of 3D mesh points.School of ComputingSCI InstituteParameterization with spherical harmonics12713School of ComputingSCI InstituteObject Alignment / Surface HomologyMZ pairDZ pairSurface CorrespondenceSchool of ComputingSCI InstituteObject Alignment prior to Shape Analysis1stelli TR, no scal 1stelli TR, vol scal Procrustes TRStoptopsidesideSchool of ComputingSCI InstituteCorrespondence through parameter space rotation• Normalization using first order ellipsoid: • Rotation of parameter space to align major axis• Spatial alignment to major axesParameters rotated to first order ellipsoidsSchool of ComputingSCI InstituteReference• [1]. Parametrization of closed surfaces for 3-D shape description, Ch. Brechbuhler, G.Gerig and O.Kubler, Communication Technology Laboratory Image Science, ETH, March 29, 1996• [2]. Description and analysis of 3-D shapes by parametrization of closed surfaces, Christian Michael Brechbuhler-Miskuv, Ph.Dthesis,Diss. ETH No. 10979• [3] Elastic Model-Based Segmentation of 2-D and 3-D Neuroradiological Data Sets, Andras Kelemen, Ph.D thesis• [4] Slides from Dr. Guido
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