An introduction to solid modeling
An introduction to solid modeling
r-regular shape reconstruction from unorganized points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Photo tourism: exploring photo collections in 3D
ACM SIGGRAPH 2006 Papers
Stability and Computation of Topological Invariants of Solids in ${\Bbb R}^n$
Discrete & Computational Geometry
Provably correct reconstruction of surfaces from sparse noisy samples
Pattern Recognition
Fast and Accurate 3D Edge Detection for Surface Reconstruction
Proceedings of the 31st DAGM Symposium on Pattern Recognition
| Hi-index | 0.10 |
Volume-based boundary reconstruction processes often have to deal with non-manifold shapes. Even though many reconstruction algorithms have been proposed for non-manifold surfaces, they usually do not preserve topological properties. Only recently, methods were presented which-given a finite set of surface sample points-result in a mesh representation of the original boundary preserving all or certain neighborhood relations, even if the sampling is sparse and highly noise corrupted. We show that the required sampling conditions of the algorithm called ''refinement reduction'' limit the guaranteed correctness of the outcome to a small class of shapes. We define new locally adaptive sampling conditions that depend on our new pruned medial axis and finally prove without any restriction on shapes that under these new conditions, the result of ''refinement reduction'' corresponds to a refinement of a topologically correct mesh in cases where the previous sampling criteria failed. Based on our results we propose a new criterion for locally adaptive point set decimation. We also discuss why our sampling conditions can only lead to a refinement of a correct reconstruction but not necessarily to a correct reconstruction itself.