Shape Analysis of Brain Ventricles Using SPHARM
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
Landmark matching via large deformation diffeomorphisms
IEEE Transactions on Image Processing
Inverse-Consistent Surface Mapping with Laplace-Beltrami Eigen-Features
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Cortical Shape Analysis in the Laplace-Beltrami Feature Space
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
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In this paper we propose a novel approach for the mapping of 3D surfaces. With the Reeb graph of Laplace-Beltrami eigenmaps, our method automatically detects stable landmark features intrinsic to the surface geometry and use them as boundary conditions to compute harmonic maps to the unit sphere. The resulting maps are diffeomorphic, robust to natural pose variations, and establish correspondences for geometric features shared across population. In the experiments, we demonstrate our method on three subcortical structures: the hippocampus, putamen, and caudate nucleus. A group study is also performed to generate a statistically significant map of local volume losses in the hippocampus of patients with secondary progressive multiple sclerosis.