Departmental Papers (CIS)

Date of this Version

May 2004

Document Type

Journal Article


Copyright 2004 IEEE. Reprinted from IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 26, Issue 5, May 2004, pages 667-671.
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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 [1]. 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.


VC-dimension, sensor placement, sampling, visibility



Date Posted: 01 November 2004

This document has been peer reviewed.