Consensus Maximisation Using Influences of Monotone Boolean Functions

Tennakoon, Ruwan; Suter, David; Zhang, Erchuan; Chin, Tat-Jun; Bab–Hadiashar, Alireza

doi:10.1109/cvpr46437.2021.00289

Cited by 9 publications

(26 citation statements)

References 28 publications

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“…The closest work to ours is [19], who proposed a quantum solution for robust fitting. However, there are nontrivial differences: first, [19] estimates per-point influences (a measure of outlyingness) [68,69] for outlier removal instead of consensus maximisation. Second, their algorithm is based on the gate computing model, which is fundamentally different from the quantum annealing approach adopted in our work.…”

Section: Related Workmentioning

confidence: 99%

A Hybrid Quantum-Classical Algorithm for Robust Fitting

Doan¹,

Sasdelli²,

Suter³

et al. 2022

Preprint

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Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is therefore critical to develop novel approaches that can bridge the gap between exact solutions that are costly, and fast heuristics that offer no quality assurances. In this paper, we propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs and terminates with a global solution or an error bound. The combinatorial subproblems are amenable to a quantum annealer, which helps to tighten the bound efficiently. While our usage of quantum computing does not surmount the fundamental intractability of robust fitting, by providing error bounds our algorithm is a practical improvement over randomised heuristics. Moreover, our work represents a concrete application of quantum computing in computer vision. We present results obtained using an actual quantum computer (D-Wave Advantage) and via simulation 1 .

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Section: Related Workmentioning

confidence: 99%

A Hybrid Quantum-Classical Algorithm for Robust Fitting

Doan¹,

Sasdelli²,

Suter³

et al. 2022

Preprint

Self Cite

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“…Recently, Tennakoon et al [24] characterized the maximum consensus problem by Monotone Boolean Function Theory and investigated the characterisation of the MaxCon solutions by influences of a monotone Boolean function. In detail, any subset I ⊆ X = {x x x i } n i=1 can be represented by a bit vector b b b of length n, where its i-th component b i = 0 denotes the exclusion of the datum x x x i and b i = 1 denotes the inclusion of the datum x x x i .…”

Section: Influence and Consensus Maximisationmentioning

confidence: 99%

“…The key concept in [24] is influence. When endowing the Boolean cube with a uniform measure, the influence of b i of a Boolean function f is defined [19] as, To estimate the influences in equation ( 3), the most obvious and natural way would be to uniformly sample, and use the empirical counts as (unbiased) estimates.…”

Section: Influence and Consensus Maximisationmentioning

confidence: 99%

“…This work directly follows [24] -here examining alternative definitions of influences and associated estimation methods. That work, in turn, uses the same basic "tree" strategy of Chin et al [4], which used A * search on a tree structure, founded on the notion of "basis" in LP-type theory.…”

Section: Introductionmentioning

confidence: 99%

“…Like many learning based approaches, it may take a long time to train and it is hard to analyse the method and its ability to generalise. Like [25] and [24], modifications to the basic tree search that lose the priority queue guarantees of A * , sacrifice optimality guarantees for speed. This paper is also spiritually in that context.…”

Section: Introductionmentioning

confidence: 99%

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Maximum Consensus by Weighted Influences of Monotone Boolean Functions

Zhang¹,

Suter²,

Tennakoon³

et al. 2021

Preprint

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Robust model fitting is a fundamental problem in computer vision: used to pre-process raw data in the presence of outliers. Maximisation of Consensus (MaxCon) is one of the most popular robust criteria and widely used. Recently (Tennakoon et al. CVPR2021), a connection has been made between MaxCon and estimation of influences of a Monotone Boolean function. Equipping the Boolean cube with different measures and adopting different sampling strategies (two sides of the same coin) can have differing effects: which leads to the current study. This paper studies the concept of weighted influences for solving MaxCon. In particular, we study endowing the Boolean cube with the Bernoulli measure and performing biased (as opposed to uniform) sampling. Theoretically, we prove the weighted influences, under this measure, of points belonging to larger structures are smaller than those of points belonging to smaller structures in general. We also consider another "natural" family of sampling/weighting strategies, sampling with uniform measure concentrated on a particular (Hamming) level of the cube.Based on weighted sampling, we modify the algorithm of Tennakoon et al., and test on both synthetic and real datasets. This paper is not promoting a new approach per se, but rather studying the issue of weighted sampling. Accordingly, we are not claiming to have produced a superior algorithm: rather we show some modest gains of Bernoulli sampling, and we illuminate some of the interactions between structure in data and weighted sampling.

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