Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Smoothing and matching of 3-D space curves
International Journal of Computer Vision
Tracking level sets by level sets: a method for solving the shape from shading problem
Computer Vision and Image Understanding
International Journal of Computer Vision
Finding Shortest Paths on Surfaces Using Level Sets Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking Points on Deformable Objects Using Curvature Information
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Curves Matching Using Geodesic Paths
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Optimal subpixel matching of contour chains and segments
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Matching of 3-D curves using semi-differential invariants
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
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A general formulation for geodesic distance propagation of surfaces is presented. Starting from a surface lying on a 3-manifold in IR4, we set up a partial differential equation governing the propagation of surfaces at equal geodesic distance (on the 3-manifold) from the given original surface. This propagation scheme generalizes a result of Kimmel et al. [11] and provides a way to compute distance maps on manifolds. Moreover, the propagation equation is generalized to any number of dimensions. Using an eulerian formulation with level-sets, it gives stable numerical algorithms for computing distance maps. This theory is used to present a new method for surface matching which generalizes a curve matching method [5]. Matching paths are obtained as the orbits of the vector field defined as the sum of two distance maps' gradient values. This surface matching technique applies to the case of large deformation and topological changes.