Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Optimization of brain conformal mapping with landmarks
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Multi-Atlas Segmentation with Joint Label Fusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper we develop a novel approach for computing conformal maps between anatomical surfaces with the ability of aligning anatomical features and achieving greatly reduced metric distortion. In contrast to conventional approaches that focused on conformal maps to the sphere or plane, our method computes the conformal map between surfaces in the embedding space formed the intrinsically defined Laplace-Beltrami (LB) eigenfunctions. Utilizing the power of LB eigenfunctions as informative descriptors of global geometry, the conformal maps computed by our method can effectively align anatomical features on cortical surfaces. By computing such feature-aware conformal maps to a group-wisely optimal atlas surface, which is also computed with metric optimization in the LB embedding space, we develop a fully automated system for cortical labeling with the fusion of labels on a large number of atlas surfaces. In our experiments, we build our system with 40 labeled surfaces and demonstrate its excellent performance with leave-one-out cross validation. We also applied the automated labeling system to cortical surfaces reconstructed from MR scans of 50 patients with Alzheimer's disease (AD) and 50 normal controls (NC) to illustrate its robustness and effectiveness in clinical data analysis.