Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Spectral surface reconstruction from noisy point clouds
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Topologically correct 3D surface reconstruction and segmentation from noisy samples
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Topologically correct image segmentation using alpha shapes
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Preserving geometric properties in reconstructing regions from internal and nearby points
Computational Geometry: Theory and Applications
Pattern Recognition Letters
Smoothness of Boundaries of Regular Sets
Journal of Mathematical Imaging and Vision
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Automated three-dimensional surface reconstruction is a very large and still fast growing area of applied computer vision and there exists a huge number of heuristic algorithms. Nevertheless, the number of algorithms which give formal guarantees about the correctness of the reconstructed surface is quite limited. Moreover such theoretical approaches are proven to be correct only for objects with smooth surfaces and extremely dense samplings with no or very few noise. We define an alternative surface reconstruction method and prove that it preserves the topological structure of multi-region objects under much weaker constraints and thus under much more realistic conditions. We derive the necessary error bounds for some digitization methods often used in discrete geometry, i.e. supercover and m-cell intersection sampling. We also give a detailed analysis of the behavior of our algorithm and compare it with other approaches.