The Minimum Cost Connected Subgraph Problem in Medical Image Analysis

Rempfler, Markus; Andres, Bjoern; Menze, Bjoern

doi:10.1007/978-3-319-46726-9_46

Cited by 6 publications

(5 citation statements)

References 12 publications

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“…One example is articulated human body pose estimation for a single human in the optimization framework of [29] where every pair of active nodes necessarily belongs to the same human. Another example is connected foreground segmentation [27,30,34,38] in which every pair of distinct foreground pixels necessarily belongs to the same segment.…”

Section: (Dis-)connectedness Constraintsmentioning

confidence: 99%

Joint Graph Decomposition & Node Labeling: Problem, Algorithms, Applications

Levinkov

Uhrig

Tang

et al. 2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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105

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We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks, including instance-separating semantic segmentation, articulated human body pose estimation and multiple object tracking. Conceptually, the problem we state generalizes the unconstrained integer quadratic program and the minimum cost lifted multicut problem, both of which are NPhard. In order to find feasible solutions efficiently, we define two local search algorithms that converge monotonously to a local optimum, offering a feasible solution at any time. To demonstrate their effectiveness in tackling computer vision tasks, we apply these algorithms to instances of the problem that we construct from published data, using published algorithms. We report state-of-the-art application-specific accuracy for the three above-mentioned applications.

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Section: (Dis-)connectedness Constraintsmentioning

confidence: 99%

Joint Graph Decomposition & Node Labeling: Problem, Algorithms, Applications

Levinkov

Uhrig

Tang

et al. 2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

Self Cite

105

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“…Although the general formulation works for multi-label MRFs, the authors applied it only to binary MRF problems. In [16], the authors optimized exactly a linear (unary-potential) objective subject to connectivity constraint in a binary segmentation problem. It solves two instances of medical benchmark datasets to optimality for the first time.…”

Section: Related Workmentioning

confidence: 99%

“…The K-Nearest strategy is reported in [16] to be one of the most successful (among five) in terms of solved instances and computational efficiency. We will adopt this vertex separation strategy in Sec.…”

Section: Ilp-pcb: Ilp-pc With Background Labelmentioning

confidence: 99%

An ILP Solver for Multi-label MRFs with Connectivity Constraints

Shen¹,

Kendinibilir²,

Ayed³

et al. 2017

Preprint

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Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., [1,2]. In these works, only Linear Programing (LP) relaxations [1,2] or simplified versions [3] of the problem were solved. This paper investigates the ILP of multi-label MRF with exact connectivity priors via a branch-and-cut method, which provably finds globally optimal solutions. The method enforces connectivity priors iteratively by a cutting plane method, and provides feasible solutions with a guarantee on sub-optimality even if we terminate it earlier. The proposed ILP can be applied as a post-processing method on top of any existing multi-label segmentation approach. As it provides globally optimal solution, it can be used off-line to generate ground-truth labeling, which serves as quality check for any fast on-line algorithm. Furthermore, it can be used to generate groundtruth proposals for weakly supervised segmentation.

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“…Graph is construction that have a long history in science that applied in pretty much every logical and building, many picture division techniques use graph construction when speaking to picture [1][2][3]. By using mathematical methods, the solution of the problem in a picture is found in a simple and adaptable manner.…”

Section: Introductionmentioning

confidence: 99%

Clotting detection in the vascular network

Salman

Abd-Almeer

2020

IJEECS

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<p>A lot of side effects accusers which the humans have suffered from a scan either by CT phrases, rays and magnetic resonance. Different methods were used to eliminate these affects depends on segmentation of vascular networks then represents it as a graph, where the intersection of the vessel as a vertex and the line between them as an edge. The place of the clot can be found by representing the weight of each edge as the amount of the blood in the vessel. Sign the place; if the amount is less than the normal flux that represents thrombosis. An algorithm in a graph theory is used to find the minimum distance, if more than one thrombosis exists to reach the nearest one and sign it alternately.</p>

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The Minimum Cost Connected Subgraph Problem in Medical Image Analysis

Cited by 6 publications

References 12 publications

Joint Graph Decomposition & Node Labeling: Problem, Algorithms, Applications

Joint Graph Decomposition & Node Labeling: Problem, Algorithms, Applications

An ILP Solver for Multi-label MRFs with Connectivity Constraints

Clotting detection in the vascular network

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