  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.
