Issue No. 05 - May (2004 vol. 26)
Volkan Isler , IEEE
Kostas Daniilidis , IEEE
<p><b>Abstract</b>—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 <it>exterior</it> 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.</p>
VC-dimension, sensor placement, sampling, visibility.
S. Kannan, V. Isler, K. Daniilidis and P. Valtr, "VC-Dimension of Exterior Visibility," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 26, no. , pp. 667-671, 2004.