Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms
International Journal of Computer Vision
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Stereo Matching Using Belief Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Efficient Graph-Based Image Segmentation
International Journal of Computer Vision
Efficient Belief Propagation for Early Vision
International Journal of Computer Vision
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
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Recent work on early vision such as image segmentation, image restoration, stereo matching, and optical flow models these problems using Markov Random Fields. Although this formulation yields an NP-hard energy minimization problem, good heuristics have been developed based on graph cuts and belief propagation. Nevertheless both approaches still require tens of seconds to solve stereo problems on recent PCs. Such running times are impractical for optical flow and many image segmentation and restoration problems. We show how to reduce the computational complexity of belief propagation by applying the Four Color Theorem to limit the maximum number of labels in the underlying image segmentation to at most four. We show that this provides substantial speed improvements for large inputs to a variety of vision problems, while maintaining competitive result quality.