Abstract
Although the triangle non-symmetry and anti-packing model (TNAM) representation for gray images is an effective image representation method, there is still much space left for optimization. In this paper, inspired by the optimization idea of the packing problem, we proposed an improved algorithm for gray image representation using the non-symmetry and anti-packing model with triangles and rectangles (NAMTR). By comparing the representation algorithm of the NAMTR with those of the TNAM and the popular linear quadtree, theoretical and experimental results presented in this paper show that the former can greatly reduce the number of sub-patterns or nodes and simultaneously save the data storage much more effectively than the latter, and therefore it is a better method to represent gray images. Representation method of the NAMTR, as envisaged in this paper, shows a very strong promise, and it is valuable for further theoretical research and potential business foreground, such as reducing storage space, increasing transmission speed and improving pattern match efficiency.
Similar content being viewed by others
References
Chen C B, He D H. Heuristic method for solving triangle packing problem. Journal of Zhejiang University, 2005, 6(6): 565–570
Krivelevich M. On a conjecture of Tuza about packing and covering of triangles. Discrete Mathematics, 1995, 142(1): 281–286
Chen C B, He D H, Hang W Q. An approximation algorithm for solving the problem of packing unit equilateral triangles in a square. Chinese Journal of Computers, 2003, 26(2): 212–220 (in Chinese)
Wu Y L, Huang WQ, Lau S C, et al. An effective quasi-human based heuristic for solving the rectangle packing problem. European Journal of Operational Research, 2002, 141(2): 341–358
Chen M, Huang W Q. A two-level search algorithm for 2D rectangular packing problem. Computers and Industrial Engineering, 2007, 53(1): 123–136
Huang WQ, Li Y, Akeb H, et al. Greedy algorithms for packing unequal circles into a rectangular container. Journal of the Operational Research Society, 2005, 56(5): 539–548
Klinger A. Data structure and pattern recognition. In: Proceedings of International Joint Conference on Pattern Recognition (IJCPR), Washington, D.C., USA, 1973, 497–498
Gargantini I. An effective way to represent quadtrees. Communications of the ACM, 1982, 25(12): 905–910
Wang C L, Wu S C, Chang Y K. quadtree and statistical model-based lossless binary image compression method. Imaging Science Journal, 2005, 53(2): 95–103
Laszlo M, Mukherjee S. A genetic algorithm using hyper-quadtrees for low-dimensional k-means clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(4): 533–543
Zheng Y P, Chen C B. A color image representation method based on non-symmetry and anti-packing model. Journal of Software, 2007, 18 (11): 2932–2941 (in Chinese)
Chen C B, Hu W J, Wan L. Direct non-symmetry and antipacking pattern representation model of medical images. In: Proceedings of the 1st International Conference on Bioinformatics and Biomedical Engineering, Wuhan, China, 2007, 1011–1018
Zheng Y P, Chen C B, Sarem M. A novel algorithm for triangle non-symmetry and anti-packing pattern representation model of gray images. In: Proceedings of the 3rd International Conference on Intelligent Computing, Lecture Note in Computer Science, Vol 4681, Qingdao, China, 2007, 832–841
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zheng, Y., Chen, C. & Sarem, M. An improved algorithm for gray image representation using non-symmetry and anti-packing model with triangles and rectangles. Front. Comput. Sci. China 2, 431–437 (2008). https://doi.org/10.1007/S11704-008-0036-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/S11704-008-0036-5