Art gallery theorems and algorithms
Art gallery theorems and algorithms
The visual potential: one convex polygon
Computer Vision, Graphics, and Image Processing
An Optimal Algorithm for Detecting Weak Visibility of a Polygon
IEEE Transactions on Computers
Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
Journal of Algorithms
Planning for complete sensor coverage in inspection
Computer Vision and Image Understanding
A survey of automated visual inspection
Computer Vision and Image Understanding
A randomized art-gallery algorithm for sensor placement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
View planning for automated three-dimensional object reconstruction and inspection
ACM Computing Surveys (CSUR)
Heuristics for the Generation of Random Polygons
Proceedings of the 8th Canadian Conference on Computational Geometry
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
VC-Dimension of Exterior Visibility
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automated camera layout to satisfy task-specific and floor plan-specific coverage requirements
Computer Vision and Image Understanding - Special issue on omnidirectional vision and camera networks
Guarding galleries and terrains
Information Processing Letters
Optimal positioning of sensors in 3d
CIARP'05 Proceedings of the 10th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis and Applications
Automatic sensor placement for model-based robot vision
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Some NP-hard polygon decomposition problems
IEEE Transactions on Information Theory
An algorithm for finding a maximum clique in a graph
Operations Research Letters
An exact algorithm for the maximum clique problem
Operations Research Letters
A new lower bound for evaluating the performances of sensor location algorithms
Pattern Recognition Letters
Polygon exploration with time-discrete vision
Computational Geometry: Theory and Applications
Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
A nearly optimal algorithm for covering the interior of an Art Gallery
Pattern Recognition
Active vision in robotic systems: A survey of recent developments
International Journal of Robotics Research
Exact solutions and bounds for general art gallery problems
Journal of Experimental Algorithmics (JEA)
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Locating visual sensors in 2D can be often modeled as an Art Gallery problem. Tasks such as surveillance require observing or ''covering'' the interior of a polygon with a minimum number of sensors or ''guards''. For other tasks, such as inspection and image based rendering, observing the boundaries of the environment is sufficient. As Interior Covering (IC), also Edge Covering (EC) is NP-hard, and no finite algorithm is known for its exact solution. Approximate EC solutions are provided by many heuristic algorithms, but their performances with respect to optimality (minimum number of sensors) is unknown. In this paper, we propose a new EC sensors location technique. The algorithm is incremental, and converges toward the optimal solution. It refines an initial approximation provided by an integer covering algorithm (IEC) where each edge is observed entirely by at least one sensor. A lower bound for the number of sensors, specific of the polygon considered, is used at each step for evaluating the quality of the current solution, and a set of rules are provided for performing a local refinement to reduce the computational burden. The algorithm has been implemented, and tests over hundreds of random polygons show that it supplies solutions very close to and often coincident with the lower bound, and then suboptimal or optimal. In addition, the approximate starting solutions provided by the IEC algorithms are, on the average, close to optimum. The tight lower bound can also be used for testing other EC sensor location algorithms. Running times allow dealing with polygons with up to a few hundreds of edges, which appears adequate for many practical cases. An enhanced version of the algorithm, also taking into account range and incidence constraints, has also been implemented and tested.