Art gallery theorems and algorithms
Art gallery theorems and algorithms
Shortest watchman routes in simple polygons
Discrete & Computational Geometry
Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
Separation and approximation of polyhedral objects
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Recovering shape by purposive viewpoint adjustment
International Journal of Computer Vision - Special issue on active vision II
A tight analysis of the greedy algorithm for set cover
Journal of Algorithms
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
On motion planning in changing, partially predictable environments
International Journal of Robotics Research
Handbook of discrete and computational geometry
Randomized query processing in robot path planning
Journal of Computer and System Sciences
A randomized art-gallery algorithm for sensor placement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
The Polygon Exploration Problem
SIAM Journal on Computing
On local transformation of polygons with visibility properties
Theoretical Computer Science
Automatic Selection of Reference Views for Image-Based Scene Representations
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Geometric Computation and the Art of Sampling
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
ICDCS '01 Proceedings of the The 21st International Conference on Distributed Computing Systems
Optimal Camera Placement for Automated Surveillance Tasks
Journal of Intelligent and Robotic Systems
A General Method for Sensor Planning in Multi-Sensor Systems: Extension to Random Occlusion
International Journal of Computer Vision
A nearly optimal sensor placement algorithm for boundary coverage
Pattern Recognition
Self-orienting wireless multimedia sensor networks for occlusion-free viewpoints
Computer Networks: The International Journal of Computer and Telecommunications Networking
New Results on Visibility in Simple Polygons
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Can you see me now? sensor positioning for automated and persistent surveillance
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Adaptive online camera coordination for multi-camera multi-target surveillance
Computer Vision and Image Understanding
A new upper bound for the VC-dimension of visibility regions
Proceedings of the twenty-seventh annual symposium on Computational geometry
Three-dimensional coverage planning for an underwater inspection robot
International Journal of Robotics Research
A new upper bound for the VC-dimension of visibility regions
Computational Geometry: Theory and Applications
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Abstract--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.