Dihedral bounds for mesh generation in high dimensions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Theory and practice of sampling and reconstruction for manifolds with boundaries
Theory and practice of sampling and reconstruction for manifolds with boundaries
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Isometric embedding of facial surfaces into S3
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Curvature analysis of frequency modulated manifolds in dimensionality reduction
Calcolo: a quarterly on numerical analysis and theory of computation
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It is often advantageous in image processing and computer vision to consider images as surfaces imbedded in higher dimensional manifolds. It is therefore important to consider the theoretical and applied aspects of proper sampling of manifolds. We present a new sampling theorem for surfaces and higher dimensional manifolds. The core of the proof resides in triangulation results for manifolds with or without boundary, not necessarily compact. The proposed method adopts a geometric approach that is considered in the context of 2-dimensional manifolds (i.e surfaces), with direct applications in image processing. Implementations of these methods and theorems are illustrated and tested both on synthetic images and on real medical data.