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## Label Configuration Priors for Continuous Multi-Label Optimization Label Configuration Priors for Continuous Multi-Label Optimization

### Citations

1292 | Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems
- Mumford, Shah
- 1989
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Citation Context ...zation problem min u∈S l s.t. (15) max p∈K n∑ i=1 ∫ Ω ui(I − ci)2 + ui div pi dx. (35) with the set S in (12) andK in (7). This energy functional is a convex relaxation of the Mumford-Shah functional =-=[11]-=-, which allows for the simultaneous optimization of the regions Ωi and the gray values. We apply this model to the segmentation of an MRI-scan in Figure 3 and compute a 2, 3 and 4 phase segmentation o... |

773 | Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multi-Band Image Segmentation
- Zhu, Yuille
- 1996
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Citation Context ...additionally imposes the information that cows are more commonly observed on grass next to the ocean than cats. A separate line of work has promoted the use of minimum description length (MDL) priors =-=[9, 17, 4, 15]-=- which imposes a prior that favors a smaller number of labels in the final segmentation. In practice, the advantage of such MDL priors is that one can preserve a level of regularity while reducing the... |

435 | T.: A first-order primal-dual algorithm for convex problems with applications to imaging
- Chambolle, Pock
- 2011
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Citation Context ...1(u) = 1 and l2(u) = 1) the supremum is 1 and is attained for µ1 = µ2 = 0.5 and the constraint (32) is active (32). Hence, we obtain ẼL(l) = EL(l). 4. Implementation We use the primal-dual algorithm =-=[2]-=- which is essentially a gradient descent in the primal variables and a gradient ascent in the dual variables with a subsequent computation of the proximity operators. For the time steps we used the re... |

109 | Fast approximate energy minimization with label costs
- Delong, Osokin, et al.
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Citation Context ...additionally imposes the information that cows are more commonly observed on grass next to the ocean than cats. A separate line of work has promoted the use of minimum description length (MDL) priors =-=[9, 17, 4, 15]-=- which imposes a prior that favors a smaller number of labels in the final segmentation. In practice, the advantage of such MDL priors is that one can preserve a level of regularity while reducing the... |

100 | P.H.S.: Graph Cut Based Inference with Co-occurrence Statistics.
- Ladicky, Russell, et al.
- 2010
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Citation Context ...arily share the same color model – horses may be white, brown or black for example. Such approaches allow to impose prior knowledge about which pairs of labels are likely to co-occur in a given image =-=[8]-=-. Figure 1 shows semantic labelings computed for the image of a cow on grass without and with a co-occurrence prior: While the data term has a slight preference for cat over cow, the co-occurrence add... |

63 |
Diagonal preconditioning for first order primal-dual algorithms in convex optimization.
- Pock, Chambolle
- 2011
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Citation Context ... descent in the primal variables and a gradient ascent in the dual variables with a subsequent computation of the proximity operators. For the time steps we used the recent preconditioning techniques =-=[12]-=-. To impose the label configuration priors, three kinds of constraints have to be implemented. • the simplex constraint ∑i ui(x) = 1 in (3) can be implemented by introducing Lagrange multipliers. a) I... |

51 | T.: A Convex Approach for Computing Minimal Partitions
- Chambolle, Cremers, et al.
- 2008
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Citation Context ...2. On the other hand, there are a number of recent advances on convex relaxation techniques for spatially continuous multi-label optimization. These include relaxations for the continuous Potts model =-=[1, 10, 16]-=-, for the non-local continuous Potts model [14], for MDL priors [15], and for vector-valued labeling problems [6, 13]. 1.3. Contribution Apart from the MDL prior, all label configuration priors have b... |

50 | Fast global labeling for real-time stereo using multiple plane sweeps. - Zach, Gallup, et al. - 2008 |

46 | Convex multi-class image labeling by simplex-constrained total variation.
- Lellmann, Kappes, et al.
- 2008
(Show Context)
Citation Context ...2. On the other hand, there are a number of recent advances on convex relaxation techniques for spatially continuous multi-label optimization. These include relaxations for the continuous Potts model =-=[1, 10, 16]-=-, for the non-local continuous Potts model [14], for MDL priors [15], and for vector-valued labeling problems [6, 13]. 1.3. Contribution Apart from the MDL prior, all label configuration priors have b... |

28 | An experimental comparison of discrete and continuous shape optimization methods
- Klodt, Schoenemann, et al.
- 2008
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Citation Context ...ion Apart from the MDL prior, all label configuration priors have been applied to the spatially discrete MRF domain, which exhibit grid bias and are hard or impossible to parallelize. As discussed in =-=[7]-=-, spatially continuous approaches do not exhibit any grid bias and respective algorithms are easily parallelized on graphics hardware. Hence, we propose a convex framework for multi-label optimization... |

15 | Tight convex relaxations for vector-valued labeling problems.
- Strekalovskiy, Goldluecke, et al.
- 2011
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Citation Context ...i-label optimization. These include relaxations for the continuous Potts model [1, 10, 16], for the non-local continuous Potts model [14], for MDL priors [15], and for vector-valued labeling problems =-=[6, 13]-=-. 1.3. Contribution Apart from the MDL prior, all label configuration priors have been applied to the spatially discrete MRF domain, which exhibit grid bias and are hard or impossible to parallelize. ... |

11 |
Tv-based multi-label image segmentation with label cost prior.
- Yuan, Boykov
- 2010
(Show Context)
Citation Context ...additionally imposes the information that cows are more commonly observed on grass next to the ocean than cats. A separate line of work has promoted the use of minimum description length (MDL) priors =-=[9, 17, 4, 15]-=- which imposes a prior that favors a smaller number of labels in the final segmentation. In practice, the advantage of such MDL priors is that one can preserve a level of regularity while reducing the... |

10 | Minimizing energies with hierarchical costs.
- Delong, Gorelick, et al.
- 2012
(Show Context)
Citation Context ...he emergence of undesired labels), for the example in Figure 1 co-occurrence is vital (since the number of labels is in both cases the same). Additionally, hierarchical priors have been introduced in =-=[3]-=-. These favor specific label groups which usually occur in the same context, e.g. a dishwasher and an oven are likely to occur together within the context of a kitchen, whereas a cow and a sheep usual... |

10 | Convex relaxation for multilabel problems with product label spaces.
- Goldluecke, Cremers
- 2010
(Show Context)
Citation Context ...i-label optimization. These include relaxations for the continuous Potts model [1, 10, 16], for the non-local continuous Potts model [14], for MDL priors [15], and for vector-valued labeling problems =-=[6, 13]-=-. 1.3. Contribution Apart from the MDL prior, all label configuration priors have been applied to the spatially discrete MRF domain, which exhibit grid bias and are hard or impossible to parallelize. ... |

5 | Region growing using the MDL principle. - Leclerc - 1990 |