B-spline knot-line elimination and Be´zier continuity conditions
Proceedings of the international conference on Curves and surfaces in geometric design
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
Statistical Study on Cortical Sulci of Human Brains
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Ridges and Ravines on Implicit Surfaces
CGI '98 Proceedings of the Computer Graphics International 1998
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Computer Vision and Image Understanding
Foreword: Discrete Differential Geometry
Computer Aided Geometric Design
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We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient algorithm, which transforms a brain surface to a single spherical spline whose maximal error deviation from the original data is less than the user-specified tolerance. Compared to the discrete mesh-based representation, our spherical spline offers a concise (low storage requirement) digital form with high continuity (Cn−−1 continuity for a degree n spherical spline). Furthermore, this representation enables the accurate evaluation of differential properties, such as curvature, principal direction, and geodesic, without the need for any numerical approximations. Thus, certain shape analysis procedures, such as segmentation, gyri and sulci tracing, and 3D shape matching, can be carried out both robustly and accurately. We conduct several experiments in order to demonstrate the efficacy of our approach for the quantitative measurement and analysis of brain surfaces.