VC-dimension of exterior visibility
In this paper, we study the Vapnik-Chervonenkis (VC)-dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VC-dimension of planar visibility systems is bounded by 23 if...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 26(2004), 5 vom: 27. Mai, Seite 667-71 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , , |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2004
|
| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Comparative Study Evaluation Study Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S. |
| Zusammenfassung: | In this paper, we study the Vapnik-Chervonenkis (VC)-dimension of set systems arising in 2D polygonal and 3D polyhedral configurations where a subset consists of all points visible from one camera. In the past, it has been shown that the VC-dimension of planar visibility systems is bounded by 23 if the cameras are allowed to be anywhere inside a polygon without holes. Here, we consider the case of exterior visibility, where the cameras lie on a constrained area outside the polygon and have to observe the entire boundary. We present results for the cases of cameras lying on a circle containing a polygon (VC-dimension= 2) or lying outside the convex hull of a polygon (VC-dimension= 5). The main result of this paper concerns the 3D case: We prove that the VC-dimension is unbounded if the cameras lie on a sphere containing the polyhedron, hence the term exterior visibility |
|---|---|
| Beschreibung: | Date Completed 26.10.2004 Date Revised 10.12.2019 published: Print Citation Status MEDLINE |
| ISSN: | 1939-3539 |