Efficient globally optimal consensus maximisation with tree search

Chin, Tat-Jun; Purkait, Pulak; Eriksson, Anders; Suter, David

doi:10.1109/cvpr.2015.7298855

Cited by 50 publications

(51 citation statements)

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“…For example in MaxFS [31], similar to SRMSD problem is formulated as a set of infeasible constraints and the goal is to find the maximum feasible subset from the set. It uses deterministic branch-and-bound (BnB) methods to find the solution but for large-scale problems, unfortunately it may take exponential time [34]. Moreover, MaxFS only guarantees solution for small-scale homogenous linear systems.…”

Section: Related Workmentioning

confidence: 99%

“…In addition, it is not supportive for SRMSD formulation as its performance is highly determined by the proportion of outliers. Another tree-based technique is recently proposed in [34] to solve the problem in reduced amount of time using application dependent heuristics and based on certain pre-assumption that residual structure is to be quasi-convex. Unfortunately, in many situations, these heuristics may not be available and the assumption on the residual structure may not be accurate in practice.…”

Section: Related Workmentioning

confidence: 99%

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GLIMPS: A Greedy Mixed-Integer Approach for Super Robust Matched Subspace Detection

Rahman

Pimentel-Alarcón

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Due to diverse nature of data acquisition and modern applications, many contemporary problems involve high dimensional datum x ∈ R d whose entries often lie in a union of subspaces and the goal is to find out which entries of x match with a particular subspace U, classically called matched subspace detection. Consequently, entries that match with one subspace are considered as inliers w.r.t the subspace while all other entries are considered as outliers. Proportion of outliers relative to each subspace varies based on the degree of coordinates from subspaces. This problem is a combinatorial NP-hard in nature and has been immensely studied in recent years. Existing approaches can solve the problem when outliers are sparse. However, if outliers are abundant or in other words if x contains coordinates from a fair amount of subspaces, this problem can't be solved with acceptable accuracy or within a reasonable amount of time. This paper proposes a twostage approach called Greedy Linear Integer Mixed Programmed Selector (GLIMPS) for this abundant-outliers setting, which combines a greedy algorithm and mixed integer formulation and can tolerate over 80% outliers, outperforming the state-of-the-art.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

GLIMPS: A Greedy Mixed-Integer Approach for Super Robust Matched Subspace Detection

Rahman

Pimentel-Alarcón

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…The weaknesses of sub-optimal methods motivate researchers to investigate globally optimal methods; however, so far they are effective on only small input sizes (small d, N and/or number of outliers o). One of the most efficient exact methods is tree search [15,5,6] (others surveyed later in Sec. 1.1), which fits (1) into the framework of the LPtype methods [25,18].…”

Section: Introductionmentioning

confidence: 99%

“…1.1), which fits (1) into the framework of the LPtype methods [25,18]. By using heuristics to guide the tree search and conduct branch pruning, A* tree search [5,6] has been demonstrated to be much faster than Breadth-First Search (BFS) and other types of globally optimal algorithms. In fact, tree search is provably fixed-parameter tractable (FPT) [4].…”

Section: Introductionmentioning

confidence: 99%

Consensus Maximization Tree Search Revisited

Cai

Chin

Koltun

2019

2019 IEEE/CVF International Conference on Computer Vision (ICCV)

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Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is one of the most efficient exact methods, though it is still limited to small inputs. We make two key contributions towards improving A* tree search. First, we show that the consensus maximization tree structure used previously actually contains paths that connect nodes at both adjacent and non-adjacent levels. Crucially, paths connecting non-adjacent levels are redundant for tree search, but they were not avoided previously. We propose a new acceleration strategy that avoids such redundant paths. In the second contribution, we show that the existing branch pruning technique also deteriorates quickly with the problem dimension. We then propose a new branch pruning technique that is less dimension-sensitive to address this issue. Experiments show that both new techniques can significantly accelerate A* tree search, making it reasonably efficient on inputs that were previously out of reach. Demo code is available at https://github. com/ZhipengCai/MaxConTreeSearch.

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“…Global methods for consensus maximization have gathered significant attention [27,5,16,10,37,46,33], mainly because RANSAC is non-deterministic and provides no guarantee for optimality. Although the consensus maximization problem has proven to be NP-hard [14], global methods with convex model representations have shown promising results both in terms of speed and optimality [42,16]. Therefore, existing methods offer satisfactory solutions only for convex models.…”

Section: Introductionmentioning

confidence: 99%

Convex Relaxations for Consensus and Non-Minimal Problems in 3D Vision

Probst

Paudel

Chhatkuli

et al. 2019

2019 IEEE/CVF International Conference on Computer Vision (ICCV)

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In this paper, we formulate a generic non-minimal solver using the existing tools of Polynomials Optimization Problems (POP) from computational algebraic geometry. The proposed method exploits the well known Shor's or Lasserre's relaxations, whose theoretical aspects are also discussed. Notably, we further exploit the POP formulation of non-minimal solver also for the generic consensus maximization problems in 3D vision. Our framework is simple and straightforward to implement, which is also supported by three diverse applications in 3D vision, namely rigid body transformation estimation, Non-Rigid Structure-from-Motion (NRSfM), and camera autocalibration. In all three cases, both non-minimal and consensus maximization are tested, which are also compared against the state-of-the-art methods. Our results are competitive to the compared methods, and are also coherent with our theoretical analysis.The main contribution of this paper is the claim that a good approximate solution for many polynomial problems involved in 3D vision can be obtained using the existing theory of numerical computational algebra. This claim leads us to reason about why many relaxed methods in 3D vision behave so well? And also allows us to offer a generic relaxed solver in a rather straightforward way. We further show that the convex relaxation of these polynomials can easily be used for maximizing consensus in a deterministic manner. We support our claim using several experiments for aforementioned three diverse problems in 3D vision.

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Efficient globally optimal consensus maximisation with tree search

Cited by 50 publications

References 0 publications

GLIMPS: A Greedy Mixed-Integer Approach for Super Robust Matched Subspace Detection

GLIMPS: A Greedy Mixed-Integer Approach for Super Robust Matched Subspace Detection

Consensus Maximization Tree Search Revisited

Convex Relaxations for Consensus and Non-Minimal Problems in 3D Vision

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