Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
Proceedings of the sixteenth annual symposium on Computational geometry
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Shape Reconstruction with Delaunay Complex
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations
CA '95 Proceedings of the Computer Animation
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Studies in Advanced Mathematics)
Anisotropic Geodesics for Perceptual Grouping and Domain Meshing
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
On Variational Curve Smoothing and Reconstruction
Journal of Mathematical Imaging and Vision
Constraining active contour evolution via Lie Groups of transformation
IEEE Transactions on Image Processing
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In this article we extend the computational geometric curve reconstruction approach to the curves embedded in the Riemannian manifold. We prove that the minimal spanning tree, given a sufficiently dense sample, correctly reconstructs the smooth arcs which can be used to reconstruct closed and simple curves in Riemannian manifolds. The proof is based on the behavior of the curve segment inside the tubular neighborhood of the curve. To take care of the local topological changes of the manifold, the tubular neighborhood is constructed in consideration with the injectivity radius of the underlying Riemannian manifold. We also present examples of successfully reconstructed curves and show applications of curve reconstruction to ordering motion frames.