We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships between nearby pixels and another is a dense graph that captures pairwise similarity between all pairs of pixels. We extend the spectral method for Normalized Cuts to this setting by combining the transition matrices of Markov chains associated with each graph. We also derive an efficient method for sparsifying the dense graph of appearance relationships. This leads to a practical algorithm for segmenting high-resolution images. The resulting method can segment challenging images without any filtering or pre-processing.
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