In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisel...In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings; 3) Every overlap graph O(G, C) is a bipartite graph and G has only one C-bridge H such that C U H is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C. This extends the results of C Thomassen's work on LEW-embedded graphs.展开更多
Human's real life is within a colorful world. Compared to the gray images, color images contain more information and have better visual effects. In today's digital image processing, image segmentation is an im...Human's real life is within a colorful world. Compared to the gray images, color images contain more information and have better visual effects. In today's digital image processing, image segmentation is an important section for computers to "understand" images and edge detection is always one of the most important methods in the field of image segmentation. Edges in color images are considered as local discontinuities both in color and spatial domains. Despite the intensive study based on integration of single-channel edge detection results, and on vector space analysis, edge detection in color images remains as a challenging issue.展开更多
基金Supported by NNSF of China(10271048,10671073)Supported by Science and Technology Commission of Shanghai Municipality(07XD14011)Supported by Shanghai Leading Academic Discipline Project(B407)
文摘In this paper, we show that for a locally LEW-embedded 3-connected graph G in orientable surface, the following results hold: 1) Each of such embeddings is minimum genus embedding; 2) The facial cycles are precisely the induced nonseparating cycles which implies the uniqueness of such embeddings; 3) Every overlap graph O(G, C) is a bipartite graph and G has only one C-bridge H such that C U H is nonplanar provided C is a contractible cycle shorter than every noncontractible cycle containing an edge of C. This extends the results of C Thomassen's work on LEW-embedded graphs.
基金National Natural Science Foundation of China (No.60374071)
文摘Human's real life is within a colorful world. Compared to the gray images, color images contain more information and have better visual effects. In today's digital image processing, image segmentation is an important section for computers to "understand" images and edge detection is always one of the most important methods in the field of image segmentation. Edges in color images are considered as local discontinuities both in color and spatial domains. Despite the intensive study based on integration of single-channel edge detection results, and on vector space analysis, edge detection in color images remains as a challenging issue.