A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Alpha-shapes and flow shapes are homotopy equivalent
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
A geometric convection approach of 3-D reconstruction
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A greedy Delaunay-based surface reconstruction algorithm
The Visual Computer: International Journal of Computer Graphics
Identifying flat and tubular regions of a shape by unstable manifolds
Proceedings of the 2006 ACM symposium on Solid and physical modeling
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
A sampling theory for compact sets in Euclidean space
Proceedings of the twenty-second annual symposium on Computational geometry
Medial axis approximation and unstable flow complex
Proceedings of the twenty-second annual symposium on Computational geometry
Stability and Computation of Topological Invariants of Solids in ${\Bbb R}^n$
Discrete & Computational Geometry
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Robust construction of the three-dimensional flow complex
Proceedings of the twenty-fourth annual symposium on Computational geometry
Reconstruction Using Witness Complexes
Discrete & Computational Geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
Feature-Preserving Reconstruction of Singular Surfaces
Computer Graphics Forum
A parallel algorithm for computing the flow complex
Proceedings of the twenty-ninth annual symposium on Computational geometry
Hi-index | 0.00 |
Reconstructing a 3D shape from sample points is a central problem faced in medical applications, reverse engineering, natural sciences, cultural heritage projects, etc. While these applications motivated intense research on 3D surface reconstruction, the problem of reconstructing more general shapes hardly received any attention. This paper develops a reconstruction algorithm changing the 3D reconstruction paradigm as follows. First, the algorithm handles general shapes, i.e. compact sets, as opposed to surfaces. Under mild assumptions on the sampling of the compact set, the reconstruction is proved to be correct in terms of homotopy type. Second, the algorithm does not output a single reconstruction but a nested sequence of plausible reconstructions. Third, the algorithm accommodates topological persistence so as to select the most stable features only. Finally, in case of reconstruction failure, it allows the identification of under-sampled areas, so as to possibly fix the sampling. These key features are illustrated by experimental results on challenging datasets, and should prove instrumental in enhancing the processing of such datasets in the aforementioned applications.