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* 1.Maniford Ranking The graph-based ranking problem is described as follows: given a node as a query, the remaining nodes are ranked based on their relevances to the given query. X : a dataset ,{x1, ...,xl,xl+1,...,xn}∈ Rm×n f : a ranking value fi to each point xi. Y: indication vector Yi=1 if xi is a query, and Yi =0 otherwise. graph G=(V,E ): the nodes V are the dataset X and the edges E are weighted by an af?nity matrix W . D: a degree matrix ,diag{d11,...,dnn}, where dii=∑jwij . * α =1/(1+ μ), S is the normalized Laplacian matrix,S=D?1/2WD?1/2. We measure the saliency of nodes using the normalized ranking score ??f* when salient queries are given, and using 1 ? ??f*when background queries are given. * 2.Graph Construction We use a k-regular graph to exploit the spatial relationship. In this work, the weight between two nodes is de?ned by: * 3.Two-Stage Saliency Detection we construct four saliency maps using boundary priors and then integrate them for the ?nal map, which is referred as the separation/combination (SC) approach. Taking top image boundary as an example, we use the nodes on this side as the queries and other nodes as the unlabelled data. Thus, the indicator vector y is given, and all the nodes are ranked based on Eq. 3 in f?.We normalize this vector to the range between 0 and 1, and the saliency map using the top boundary prior, St can be written as: 3.1Ranking with Background Queries * The four saliency maps are integrated by the following process: To improve the results especially when objects appear near the image boundaries, the saliency maps are further improved via ranking with foreground queries. * Step1:Binary segment the saliency map of the ?rst stage facilitates Step2:selecting the nodes of the foreground salient objects as queries. We expect that the selected queries cover the salient object regions as much as possible. 3.2Ranking with Foreground Queries * * * *
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