The Conditional Random Field (CRF) is a popular tool for object-based image segmentation. CRFs used in practice typically have edges only between adjacent image pixels. To represent object relationship statistics beyond adjacent pixels, prior work either represents only weak spatial information using the segmented regions, or encodes only global object co-occurrences. In this paper, we propose a unified model that augments the pixel-wise CRFs to capture object spatial relationships. To this end, we use a fully connected CRF, which has an edge for each pair of pixels. The edge potentials are defined to capture the spatial information and preserve the object boundaries at the same time. Traditional inference methods, such as belief propagation and graph cuts, are impractical in such a case where billions of edges are defined. Under only one assumption that the spatial relationships among different objects only depend on their relative positions (spatially stationary), we develop an efficient inference algorithm that converges in a few seconds on a standard resolution image, where belief propagation takes more than one hour for a single iteration.
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