Name
Abstract | ||
|---|---|---|
We define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly convex regions. The decomposition is applied without explicitly measuring the convexity rank. The method merely amounts to a spectral clustering of a matrix representing the all-pairs line of sight. Our method can be directly applied on an oriented point cloud and does not require any topological information, nor explicit concavity or convexity measures. We demonstrate the efficiency of our algorithm on a large number of examples and compare them qualitatively with competitive approaches. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1111/cgf.12169 | Comput. Graph. Forum |
Keywords | Field | DocType |
spectral method,all-pairs line,large number,total number,weak convexity,spectral clustering,explicit concavity,weak convex decomposition,competitive approach,convexity measure,convexity rank | Spectral clustering,Mathematical optimization,Combinatorics,Convexity,Matrix (mathematics),Sight,Regular polygon,Spectral method,Line-of-sight,Point cloud,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 5 | 0167-7055 |
Citations | PageRank | References |
22 | 0.75 | 18 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shmuel Asafi | 1 | 22 | 1.08 |
| Avi Goren | 2 | 22 | 0.75 |
| Daniel Cohen-Or | 3 | 10588 | 533.55 |