Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
International Journal of Computer Vision
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
SMI 2012: Full Posture-invariant statistical shape analysis using Laplace operator
Computers and Graphics
Temporal shape analysis via the spectral signature
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
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This paper proposes to use the volumetric Laplace spectrum as a global shape descriptor for medical shape analysis. The approach allows for shape comparisons using minimal shape preprocessing. In particular, no registration, mapping, or remeshing is necessary. All computations can be performed directly on the voxel representations of the shapes. The discriminatory power of the method is tested on a population of female caudate shapes (brain structure) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the volumetric Laplace spectrum are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann spectra. Both, the computations of spectra on 3D voxel data for shape matching as well as the use of the Neumann spectrum for shape analysis are completely new.