Computational geometry: an introduction
Computational geometry: an introduction
On shortest paths in polyhedral spaces
SIAM Journal on Computing
Shortest paths on polyhedral surfaces
Proceedings on STACS 85 2nd annual symposium on theoretical aspects of computer science
SIAM Journal on Computing
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Computational Surface Flattening: A Voxel-Based Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Surface Flattening: A Voxel-Based Approach
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
3D brain surface matching based on geodesics and local geometry
Computer Vision and Image Understanding - Special issue on nonrigid image registration
Planar development of free-form surfaces: quality evaluation and visual inspection
Computing - Geometric modelling dagstuhl 2002
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Texture mapping via spherical multi-dimensional scaling
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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The authors implement an algorithm that finds minimal (geodesic) distances on a three-dimensional polyhedral surface. The algorithm is intrinsically parallel, in as much as it deals with all nodes simultaneously, and is simple to implement. Although exponential in complexity, it can be used with a companion gradient-descent surface-flattening algorithm that produces an optimal flattening of a polyhedral surface. Together, these two algorithms have made it possible to obtain accurate flattening of biological surfaces consisting of several thousand triangular faces (monkey visual cortex) by providing a characterization of the distance geometry of these surfaces. The authors propose this approach as a pragmatic solution to characterizing the surface geometry of the complex polyhedral surfaces which are encountered in the cortex of vertebrates.