Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maxim...Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maximum size of a partition of E(G) into edgecovers of G. It is known that for any graph G with minimum degree δ,δ- 1 The fractional edge covering chromatic number of a graph G, denoted by Xcf(G), is thefractional matching number of the edge covering hypergraph H of G whose vertices arethe edges of G and whose hyperedges the edge covers of G. In this paper, we studythe relation between X’c(G) and δ for any graph G, and give a new simple proof of theinequalities δ - 1 ≤ X’c(G) ≤ δ by the technique of graph coloring. For any graph G, wegive an exact formula of X’cf(G), that is,where A(G)=minand the minimum is taken over all noempty subsets S of V(G) and C[S] is the set of edgesthat have at least one end in S.展开更多
We present the analysis of three independent and most widely used image smoothing techniques on a new fractional based convolution edge detector originally constructed by same authors for image edge analysis. The impl...We present the analysis of three independent and most widely used image smoothing techniques on a new fractional based convolution edge detector originally constructed by same authors for image edge analysis. The implementation was done using only Gaussian function as its smoothing function based on predefined assumptions and therefore did not scale well for some types of edges and noise. The experiments conducted on this mask using known images with realistic geometry suggested the need for image smoothing adaptation to obtain a more optimal performance. In this paper, we use the structural similarity index measure and show that the adaptation technique for choosing smoothing function has significant advantages over a single function implementation. The new adaptive fractional based convolution mask can smoothly find edges of various types in detail quite significantly. The method can now trap both local discontinuities in intensity and its derivatives as well as locating Dirac edges.展开更多
基金the National Natural Science Foundation the Doctoral Foundation of the Education Committee of China.
文摘Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maximum size of a partition of E(G) into edgecovers of G. It is known that for any graph G with minimum degree δ,δ- 1 The fractional edge covering chromatic number of a graph G, denoted by Xcf(G), is thefractional matching number of the edge covering hypergraph H of G whose vertices arethe edges of G and whose hyperedges the edge covers of G. In this paper, we studythe relation between X’c(G) and δ for any graph G, and give a new simple proof of theinequalities δ - 1 ≤ X’c(G) ≤ δ by the technique of graph coloring. For any graph G, wegive an exact formula of X’cf(G), that is,where A(G)=minand the minimum is taken over all noempty subsets S of V(G) and C[S] is the set of edgesthat have at least one end in S.
文摘We present the analysis of three independent and most widely used image smoothing techniques on a new fractional based convolution edge detector originally constructed by same authors for image edge analysis. The implementation was done using only Gaussian function as its smoothing function based on predefined assumptions and therefore did not scale well for some types of edges and noise. The experiments conducted on this mask using known images with realistic geometry suggested the need for image smoothing adaptation to obtain a more optimal performance. In this paper, we use the structural similarity index measure and show that the adaptation technique for choosing smoothing function has significant advantages over a single function implementation. The new adaptive fractional based convolution mask can smoothly find edges of various types in detail quite significantly. The method can now trap both local discontinuities in intensity and its derivatives as well as locating Dirac edges.
