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Issue No. 07 - July (2010 vol. 32)
ISSN: 0162-8828
pp: 1182-1196
Xiaoqing Liu , UtopiaCompression Corporation, Los Angeles
Olga Veksler , University of Western Ontario, London
Jagath Samarabandu , University of Western Ontario, London
In the last decade, graph-cut optimization has been popular for a variety of labeling problems. Typically, graph-cut methods are used to incorporate smoothness constraints on a labeling, encouraging most nearby pixels to have equal or similar labels. In addition to smoothness, ordering constraints on labels are also useful. For example, in object segmentation, a pixel with a “car wheel” label may be prohibited above a pixel with a “car roof” label. We observe that the commonly used graph-cut \alpha-expansion move algorithm is more likely to get stuck in a local minimum when ordering constraints are used. For a certain model with ordering constraints, we develop new graph-cut moves which we call order-preserving. The advantage of order-preserving moves is that they act on all labels simultaneously, unlike \alpha-expansion. More importantly, for most labels \alpha, the set of \alpha-expansion moves is strictly smaller than the set of order-preserving moves. This helps to explain why in practice optimization with order-preserving moves performs significantly better than \alpha-expansion in the presence of ordering constraints. We evaluate order-preserving moves for the geometric class scene labeling (introduced by Hoiem et al.) where the goal is to assign each pixel a label such as “sky,” “ground,” etc., so ordering constraints arise naturally. In addition, we use order-preserving moves for certain simple shape priors in graph-cut segmentation, which is a novel contribution in itself.
Energy minimization, graph cuts, max-flow, SVM, geometric class labeling, shape prior.

O. Veksler, X. Liu and J. Samarabandu, "Order-Preserving Moves for Graph-Cut-Based Optimization," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 1182-1196, 2009.
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