Abstract
In this paper, we propose a parallel algorithm to solve the convex hull problem for an (n×n) multi-leveled image using a reconfigurable mesh connected computer of the same size as a computational model. The algorithm determines parallely the convex hull of all the connected components of the multileveled image. It is based on some geometric properties and a top-down strategy. The complexity of the algorithm is O(log n) times. Using some approximations on the component contours, this complexity is reduced to O(log m) times where m is the number of the vertices of the convex hull of the biggest component of the image.This complexity is reached thanks to the polymorphic properties of the mesh where all the components are simultaneously and separately processed.
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References
Elmesbahi, J. and Charkaoui, J.: Structure analysis for Gray level pictures on a mesh connected computer, in: Proc. of IEEE Internat. Conf. on SMC, October 1986, pp. 1415–1419.
Fu, A. M. N. and Yan, H.: Effective classification of planar shapes based on curve segment properties, Pattern Recognition Lett. 18 (1997), 55–61.
Hayachi, T. et al.: An O((log log n) 2 ) time algorithm to compute the convex hull of sorted points on reconfigurable meshes, IEEE Trans. Parallel Distributed Systems 9(12) (1998).
Jarvis, C.: Fitting polygons to figure boundary data, Austral. Comput. J. 3 (1971), 50–54.
Kim, C. E. and Stojmenović, I.: Parallel algorithms for digital geometry, CS-87-179, Washington State University, Pullman, December 1987.
Li, H. and Maresca, M.: Polymorphic torus architecture for computer vision, IEEE Trans. Pattern Anal. Mach. Intelligence 11(3) (1989), 233–242.
Ling, T. et al.: Efficient parallel processing of image contours, IEEE Trans. Pattern Anal.Mach. Intelligence 15(1) (1993), 69–81.
Miller, R. et al.: Geometric algorithms for digitized pictures on a mesh connected computer, IEEE Trans. Pattern Anal. Mach. Intelligence 7(2) (1985).
Miller, R. et al.: Meshes with reconfigurable buses, in: Proc. of the 5th MIT Conf. on Advanced Research in VLSI, Cambridge, MA, 1988, pp. 163–178.
Miller, R., Prasanna-Kummar, V. K., Reisis, D. I. and Stout, Q. F.: Parallel computation on reconfigurable meshes, IEEE Trans. Comput. 42(6) (1993), 678–692.
Miller, R. and Stout, Q. F.:Mesh computer algorithms for computational geometry, IEEE Trans. Comput. 38(3) (1989), 321–340.
Prasanna, V. K. and Reisis, D. I.: Image computation on meshes with multiple broadcast, IEEE Trans. Pattern Anal. Mach. Intelligence 11(11) (1989), 1194–1201.
Stout, Q. F.: Mapping vision algorithms to parallel architectures, Proc. IEEE (August 1988).
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Bouattane, O., Elmesbahi, J. & Rami, A. A Fast Parallel Algorithm for Convex Hull Problem of Multi-Leveled Images. Journal of Intelligent and Robotic Systems 33, 285–299 (2002). https://doi.org/10.1023/A:1015083706590
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DOI: https://doi.org/10.1023/A:1015083706590