A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Average brain models: a convergence study
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
A template free approach to volumetric spatial normalization of brain anatomy
Pattern Recognition Letters
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Robust Point Matching for Nonrigid Shapes by Preserving Local Neighborhood Structures
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust 3D Shape Correspondence in the Spectral Domain
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Global medical shape analysis using the Laplace-Beltrami spectrum
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
International Journal of Computer Vision
Discrete Calculus: Applied Analysis on Graphs for Computational Science
Discrete Calculus: Applied Analysis on Graphs for Computational Science
Fast brain matching with spectral correspondence
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Efficient population registration of 3d data
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations
International Journal of Computer Vision
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Accurate matching of cortical surfaces is necessary in many neuroscience applications. In this context diffeomorphisms are often sought, because they facilitate further statistical analysis and atlas building. Present methods for computing diffeomorphisms are based on optimizing flows or on inflating surfaces to a common template, but they are often computationally expensive. It typically takes several hours on a conventional desktop computer to match a single pair of cortical surfaces having a few hundred thousand vertices. We propose a very fast alternative based on an application of spectral graph theory on a novel association graph. Our symmetric approach can generate a diffeomorphic correspondence map within a few minutes on high-resolution meshes while avoiding the sign and multiplicity ambiguities of conventional spectral matching methods. The eigenfunctions are shared between surfaces and provide a smooth parameterization of surfaces. These properties are exploited to compute differentials on highly folded cortical surfaces. Diffeomorphisms can thus be verified and invalid surface folding detected. Our method is demonstrated to attain a vertex accuracy that is at least as good as that of FreeSurfer and Spherical Demons but in only a fraction of their processing time. As a practical experiment, we construct an unbiased atlas of cortical surfaces with a speed several orders of magnitude faster than current methods.