Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometry of harmonic maps
International Journal of Computer Vision
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Journal of Computational Physics
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Processing textured surfaces via anisotropic geometric diffusion
IEEE Transactions on Image Processing
Heat kernel smoothing using laplace-beltrami eigenfunctions
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part I
Hyperbolic harmonic brain surface registration with curvature-based landmark matching
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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Neuroimaging data, such as 3-D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3-D space.We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.