Comparison of energy minimization algorithms for highly connected graphs

V. Kolmogorov, C. Rother, in:, Springer, 2006, pp. 1–15.

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Algorithms for discrete energy minimization play a fundamental role for low-level vision. Known techniques include graph cuts, belief propagation (BP) and recently introduced tree-reweighted message passing (TRW). So far, the standard benchmark for their comparison has been a 4-connected grid-graph arising in pixel-labelling stereo. This minimization problem, however, has been largely solved: recent work shows that for many scenes TRW finds the global optimum. Furthermore, it is known that a 4-connecled grid-graph is a poor stereo model since it does not take occlusions into account. We propose the problem of stereo with occlusions as a new test bed for minimization algorithms. This is a more challenging graph since it has much larger connectivity, and it also serves as a better stereo model. An attractive feature of this problem is that increased connectivity does not result in increased complexity of message passing algorithms. Indeed, one contribution of this paper is to show that sophisticated implementations of BP and TRW have the same time and memory complexity as that of 4-connecled grid-graph stereo. The main conclusion of our experimental study is that for our problem graph cut outperforms both TRW and BP considerably. TRW achieves consistently a lower energy than BP. However, as connectivity increases the speed of convergence of TRW becomes slower. Unlike 4-connected grids, the difference between the energy of the best optimization method and the lower bound of TRW appears significant. This shows the hardness of the problem and motivates future research.
Publishing Year
Date Published
2006-05-03
Volume
3952 LNCS
Page
1 - 15
Conference
ECCV: European Conference on Computer Vision
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Kolmogorov V, Rother C. Comparison of energy minimization algorithms for highly connected graphs. In: Vol 3952 LNCS. Springer; 2006:1-15. doi:10.1007/11744047_1
Kolmogorov, V., & Rother, C. (2006). Comparison of energy minimization algorithms for highly connected graphs (Vol. 3952 LNCS, pp. 1–15). Presented at the ECCV: European Conference on Computer Vision, Springer. https://doi.org/10.1007/11744047_1
Kolmogorov, Vladimir, and Carsten Rother. “Comparison of Energy Minimization Algorithms for Highly Connected Graphs,” 3952 LNCS:1–15. Springer, 2006. https://doi.org/10.1007/11744047_1.
V. Kolmogorov and C. Rother, “Comparison of energy minimization algorithms for highly connected graphs,” presented at the ECCV: European Conference on Computer Vision, 2006, vol. 3952 LNCS, pp. 1–15.
Kolmogorov V, Rother C. 2006. Comparison of energy minimization algorithms for highly connected graphs. ECCV: European Conference on Computer Vision, LNCS, vol. 3952 LNCS. 1–15.
Kolmogorov, Vladimir, and Carsten Rother. Comparison of Energy Minimization Algorithms for Highly Connected Graphs. Vol. 3952 LNCS, Springer, 2006, pp. 1–15, doi:10.1007/11744047_1.

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