Cortical Shape Analysis using the Anisotropic Global Point Signature

We present a novel shape representation that characterizes the shape of a surface in terms of a coordinate system based on the eigensystem of the anisotropic Laplace-Beltrami operator. In contrast to the existing techniques, our representation can capture developable transformations and is therefore useful for analysis of cortical folding patterns. This representation has desirable properties including stability, uniqueness and invariance to scaling as well as isometric transformations. Additionally, the resulting shape space has a standard Euclidean metric simplifying shape analysis. We also present an approach that provides a fast and accurate computational method for solving the eigensystem using a finite element formulation. We demonstrate the utility of this representation for two brain shape analysis applications: quantifying symmetries in shape between the two cortical hemispheres and finding variance of cortical surface shapes across populations.