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
Preserving Topology by a Digitization Process
Journal of Mathematical Imaging and Vision
r-regular shape reconstruction from unorganized points
Computational Geometry: Theory and Applications - special issue on applied computational geometry
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Spectral surface reconstruction from noisy point clouds
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Topologically correct image segmentation using alpha shapes
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Provably correct reconstruction of surfaces from sparse noisy samples
Pattern Recognition
Computer Vision and Image Understanding
| Hi-index | 0.00 |
Existing theories on 3D surface reconstruction impose strong constraints on feasible object shapes and often require error-free measurements. Moreover these theories can often only be applied to binary segmentations, i.e. the separation of an object from its background. We use the Delaunay complex and a-shapes to prove that topologically correct segmentations can be obtained under much more realistic conditions. Our key assumption is that sampling points represent object boundaries with a certain maximum error. We use this in the context of digitization, i.e. for the reconstruction based on supercover and m-cell intersection samplings.