On a conjecture of Tuza about packing and covering of triangles
Discrete Mathematics
An effective way to represent quadtrees
Communications of the ACM
A Genetic Algorithm Using Hyper-Quadtrees for Low-Dimensional K-means Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The triangle packing problem has yielded many significant theories and applications such as textile cutting and container stuffing. Although the representation method of the popular linear quadtree has many merits, it puts too much emphasis upon the symmetry of image segmentation. Therefore, it is not the optimal representation method. In this paper, inspired by the concept of the triangle packing problem, we present a Triangle Nonsymmetry and Anti-packing pattern representation Model (TNAM). Also, we propose a novel algorithm for the TNAM of the gray images. By comparing the algorithm for the TNAM with that for the linear quadtree, the theoretical and experimental results show that the former is much more effective than the latter and is a better method to represent the gray images. The algorithm for the TNAM of the gray images is valuable for the theoretical research and potential business foreground.