Partial Optimality via Iterative Pruning for the Potts Model

Swoboda, Paul; Savchynskyy, Bogdan; Kappes, Jörg Hendrik; Schnörr, Christoph

doi:10.1007/978-3-642-38267-3_40

Cited by 15 publications

(28 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Swoboda et al [35] published a new algorithm to obtain partial optimality in Potts models which increases the number of known variables significantly. In future work we will employ this method, consider methods for higher order factors, methods that provide stronger partial optimality criteria, as well as methods for general pairwise terms.…”

Section: Discussionmentioning

confidence: 99%

Towards Efficient and Exact MAP-Inference for Large Scale Discrete Computer Vision Problems via Combinatorial Optimization

Kappes

Speth²,

Reinelt³

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

View full text Add to dashboard Cite

Discrete graphical models (also known as discrete Markov random fields) are a major conceptual tool to model the structure of optimization problems in computer vision. While in the last decade research has focused on fast approximative methods, algorithms that provide globally optimal solutions have come more into the research focus in the last years. However, large scale computer vision problems seemed to be out of reach for such methods.In this paper we introduce a promising way to bridge this gap based on partial optimality and structural properties of the underlying problem factorization. Combining these preprocessing steps, we are able to solve grids of size 2048 × 2048 in less than 90 seconds. On the hitherto unsolvable Chinese character dataset of Nowozin et al. we obtain provably optimal results in 56% of the instances and achieve competitive runtimes on other recent benchmark problems.While in the present work only generalized Potts models are considered, an extension to general graphical models seems to be feasible.

show abstract

Section: Discussionmentioning

confidence: 99%

Towards Efficient and Exact MAP-Inference for Large Scale Discrete Computer Vision Problems via Combinatorial Optimization

Kappes

Speth²,

Reinelt³

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

View full text Add to dashboard Cite

show abstract

“…Persistency criteria for the multilabel Potts problem that can be efficiently checked with max-flow computations have been developed in [27,28] and refined in [14]. More powerful criteria based on LP-relaxations have been proposed for the multilabel Potts problem in [41] and in [38,42,40] for general discrete MRFs. An in-depth exposition of the concept of improving mappings that is used implicitly or explicitly for all of the above MRF criteria can be found in [37].…”

Section: Related Workmentioning

confidence: 99%

Combinatorial Persistency Criteria for Multicut and Max-Cut

Lange

Andres

Swoboda

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

Self Cite

View full text Add to dashboard Cite

In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to verify them. The criteria that we derive are based on mappings that improve feasible multicuts, respectively cuts. Our elementary criteria can be checked enumeratively. The more advanced ones rely on fast algorithms for upper and lower bounds for the respective cut problems and max-flow techniques for auxiliary min-cut problems. Our methods can be used as a preprocessing technique for reducing problem sizes or for computing partial optimality guarantees for solutions output by heuristic solvers. We show the efficacy of our methods on instances of both problems from computer vision, biomedical image analysis and statistical physics.

show abstract

“…In contrast to the above methods that technically rely either on local conditions or on computing a maximum flow (min-cut), the works [42,43,44] and [35] proposed persistency approaches relying on a general linear programming relaxation. Authors of [42,43,44] demonstrated applicability of their approach to large-scale problems by utilizing existing efficient approximate MAP-inference algorithms, while in [35] the large-scale problems are addressed using a windowing technique. Despite the superior persistency results, the running time of the approximate-LP-based methods remained prohibitively slow for practical applications as illustrated by an example in Fig.…”

Section: Related Workmentioning

confidence: 99%

“…There are only two possible choices for p v : either i → y v for all i ∈ X v or the identity i → i. Methods [24,42,43] can be explained as finding an improving mapping in this class [35]. We generalize the method [43] to substitutions in P 2,y .…”

Section: Comparison To Previous Workmentioning

confidence: 99%

Maximum persistency via iterative relaxed inference with graphical models

Shekhovtsov¹,

Swoboda

Savchynskyy

2015

2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

Self Cite

View full text Add to dashboard Cite

Abstract-We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision.

show abstract

Partial Optimality via Iterative Pruning for the Potts Model

Cited by 15 publications

References 16 publications

Towards Efficient and Exact MAP-Inference for Large Scale Discrete Computer Vision Problems via Combinatorial Optimization

Towards Efficient and Exact MAP-Inference for Large Scale Discrete Computer Vision Problems via Combinatorial Optimization

Combinatorial Persistency Criteria for Multicut and Max-Cut

Maximum persistency via iterative relaxed inference with graphical models

Contact Info

Product

Resources

About