VC-dimension of exterior visibility

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 26, Issue 5, 2004, Pages 667-671

  Isler, Volkan ^a   Kannan, Sampath ^a   Daniilidis, Kostas ^a   Valtr, Pavel ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Sampling; Sensor placement; VC dimension; Visibility

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; GRAPH THEORY; IMAGE PROCESSING; OBJECT RECOGNITION; POLYNOMIALS; PROBLEM SOLVING; SENSORS; SET THEORY; THEOREM PROVING; THREE DIMENSIONAL; VISIBILITY;

EXTERIOR VISIBILITY; IMAGE BASED RENDERING; SENSOR PLACEMENT; VAPNIK-CHERVONENKIS-DIMENSION;

PATTERN RECOGNITION SYSTEMS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; CLUSTER ANALYSIS; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; CLUSTER ANALYSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SUBTRACTION TECHNIQUE;

EID: 3042632195     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2004.1273987     Document Type: Article

References (30)

1. P. Valtr, "Guarding Galleries Where No Point Sees a Small Area," Israel J. Math., vol. 104, pp. 1-16, 1998.
2. J. O'Rourke, Art Gallery Theorems And Algorithms. Oxford Univ. Press, 1987.
3. T. Shermer, "Recent Results in Art Galleries," Proc. IEEE, vol. 80, pp. 1384-1399, 1992.
4. J. O'Rourke, "Visibility," Handbook of Discrete and Computational Geometry. J.E. Goodman and J. O'Rourke eds., ch. 25, pp. 467-480, CRC Press LLC, 1997.
5. A. Acampora, "Last Mile by Laser," Scientific Am., vol. 287, pp. 48-53, July 2002.
6. W. Chin and S. Ntafos, "Shortest Watchman Routes in Simple Polygons," Discrete and Computational Geometry, vol. 6, no. 1, pp. 9-31, 1991.
7. R. Sharma and J. Molineros, "Computer Vision-Based Augmented Reality for Guiding Manual Assembly," Presence: Teleoperators and Virtual Environments, vol. 6, pp. 292-317, 1997.
8. F. Hoffmann, C. Icking, R. Klein, and K. Kriegel, "The Polygon Exploration Problem," SIAM J. Computing, vol. 31, no. 2, pp. 577-600, 2002.
9. X. Deng, T. Kameda, and C. Papadimitriou, "How to Learn an Unknown Environment i: The Rectilinear Case," J. ACM, vol. 45, pp. 215-245, 1998.
10. S.M. LaValle and R. Sharma, "On Motion Planning in Changing, Partially-Predictable Environments," Int'l J. Robotics Research, vol. 16, pp. 775-805, 1997.
11. K. Tarabanis, P. Allen, and R. Tsai, "A Survey of Sensor Planning in Computer Vision," IEEE Trans. Robotics and Automation, vol. 11, pp. 86-104, 1995.
12. K. Kutulakos and C. Dyer, "Recovering Shape by Purposive Viewpoint Adjustment," Int'l J. Computer Vision, vol. 12, pp. 113-136, 1994.
13. V. Hlavac, A. Leonardis, and T. Werner, "Automatic Selection of Reference Views for Image-Based Scene Representations," Proc. European Conf. Computer Vision, pp. 526-535, 1996.
14. N. Bulusu, J. Heidemann, and D. Estrin, "Adaptive Beacon Placement," Proc. Int'l Conf. Distributed Computing Systems, 2001.
15. V.N. Vapnik and A.Y. Chervonenkis, "On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities," Theory of Probability and Its Applications, vol. 16, no. 2, pp. 264-280, 1971.
16. J. Matousek, "Geometric Computation and the Art of Sampling," IEEE Symp. Foundations of Computer Science - Tutorial, 1998.
17. P.K. Agarwal and S. Sen, "Randomized Algorithms for Geometric Optimization Problems," Handbook of Randomization, P. Pardalos et al., eds., Kluwer Academic Publishers, 2003.
18. P. Valtr, "On Galleries with No Bad Points," Discrete & Computational Geometry, vol. 21, pp. 193-200, 1999.
19. L.E. Kavraki, J.-C. Latombe, and R. Motwani, "Randomized Query Processing in Robot Path Planning," J. Computer and System Sciences, vol. 57, pp. 50-60, Aug. 1998.
20. P. Slavik, "A Tight Analysis of the Greedy Algorithm for Set Cover," J. Algorithms, vol. 25, pp. 237-254, 1997.
21. H. Brönnimann and M. Goodrich, "Almost Optimal Set Covers in Finite VC-Dimension," Discrete & Computational Geometry, vol. 14, no. 4, pp. 463-479, 1995.
22. S. Ghosh, "Approximation Algorithms for Art Gallery Problems," Proc. Canadian Information Processing Soc. Congress, 1987.
23. H. Gonzalez-Banos and J. Latombe, "A Randomized Art-Gallery Algorithm for Sensor Placement," Proc. ACM Symp. Computational Geometry (SoCG '01), pp. 232-240, 2001.
24. S. Eidenbenz, C. Stamm, and P. Widmayer, "Inapproximability Results for Guarding Polygons and Terrains," Algorithmica, vol. 31, pp. 79-113, 2001.
25. V. Isler, S. Kannan, and K. Daniilidis, "VC-Dimension of Exterior Visibility of Polyhedra," Technical Report: MS-CIS-01-34, Computer and Information Science, Univ. of Pennsylvania, 2001.
26. J.S.B. Mitchell and S. Suri. "Separation and Approximation of Polyhedral Surfaces," Proc. Third ACM-SIAM Symp. Discrete Algorithms (SODA), pp. 296-306, 1992.
27. V.S.A. Kumar, S. Arya, and H. Ramesh, "Hardness of Set Cover with Intersection 1," Automata, Languages and Programming, pp. 624-635, 2000.
28. B. Brodén, M. Hammar, and B.J. Nilsson, "Guarding Lines and 2-Link Polygons in Apx-Hard," Proc. 13th Canadian Conf. Computational Geometry, pp. 45-48, 2001.
29. C. Hernando, M.E. Houle, and F. Hurtado, "On Local Transformation of Polygons with Visibility Properties," Theoretical Computer Science, vol. 289, pp. 919-937, Oct. 2002.
30. W. Plantiga and C. Dyer, "Visibility, Occlusion, and the Aspect Graph," Int'l J. Computer Vision, vol. 5, no. 2, pp. 137-160, 1990.