Practical and Efficient Multi-view Matching

Maset, Eleonora; Arrigoni, Federica; Fusiello, Andrea

doi:10.1109/iccv.2017.489

Cited by 54 publications

(98 citation statements)

References 25 publications

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“…Based on the confidence information we could retain multiple hypotheses. This is not possible by the other approaches such as Wang et al [59,88]. Rand-K refers to using K − 1 additional random hypotheses to complement the found solution.…”

Section: Datasetmentioning

confidence: 99%

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Probabilistic Permutation Synchronization Using the Riemannian Structure of the Birkhoff Polytope

Birdal

Şimşekli

2019

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

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We present an entirely new geometric and probabilistic approach to synchronization of correspondences across multiple sets of objects or images. In particular, we present two algorithms: (1) Birkhoff-Riemannian L-BFGS for optimizing the relaxed version of the combinatorially intractable cycle consistency loss in a principled manner, (2) Birkhoff-Riemannian Langevin Monte Carlo for generating samples on the Birkhoff Polytope and estimating the confidence of the found solutions. To this end, we first introduce the very recently developed Riemannian geometry of the Birkhoff Polytope. Next, we introduce a new probabilistic synchronization model in the form of a Markov Random Field (MRF). Finally, based on the first order retraction operators, we formulate our problem as simulating a stochastic differential equation and devise new integrators. We show on both synthetic and real datasets that we achieve high quality multi-graph matching results with faster convergence and reliable confidence/uncertainty estimates.

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Section: Datasetmentioning

confidence: 99%

“…We initialize our algorithm by the closed form MatchEIG [59] and evaluate it against the state of the art methods of Spectral [64], MatchALS [98], MatchLift [42], MatchEIG [59], and Wang et al [88]. The size of the universe is set to the number of features per image.…”

Section: Experiments and Evaluationsmentioning

confidence: 99%

Probabilistic Permutation Synchronization Using the Riemannian Structure of the Birkhoff Polytope

Birdal

Şimşekli

2019

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

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“…With this matrix notation it becomes also apparent that one can achieve synchronisation by matrix factorisation, such as pursued by the aforementioned spectral approaches [35,40,2,30]. While recently a lot of progress has been made for permutation synchronisation, one of the open problems is how to efficiently integrate higher-order information to model geometric relations between points.…”

Section: Background and Related Workmentioning

confidence: 99%

“…Multi-image matching: We compare our method with QUICKMATCH [44], MATCHEIG [30], SPECTRAL [35] (implemented by the authors of [57] for partial permutation synchronisation), and MATCHALS [57]. Other methods that incorporate geometric information [52,49,47] do not scale to such large problem instances, see Fig.…”

Section: Hippi Datasetmentioning

confidence: 99%

“…Practical approaches for solving multi-matching problems can be put into two categories: (i) methods that jointly optimise for multi-matchings between all objects (e.g. [22,49,41,44,6]) and (ii) approaches that first establish matchings between points in each pair of objects independently, and then improve those matchings via a postprocessing procedure referred to as permutation synchronisation [35,12,57,40,30]. Approaches that jointly optimise for multi-matchings either ignore geometric relations between the points [44], or are prohibitively expensive and thus only applicable to small problems (cf.…”

Section: Introductionmentioning

confidence: 99%

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HiPPI: Higher-Order Projected Power Iterations for Scalable Multi-Matching

Bernard

Thunberg

Swoboda

et al. 2019

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

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The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-matching problem is difficult. It can be phrased as simultaneously solving multiple (NP-hard) quadratic assignment problems (QAPs) that are coupled via cycle-consistency constraints. The main limitations of existing multi-matching methods are that they either ignore geometric consistency and thus have limited robustness, or they are restricted to small-scale problems due to their (relatively) high computational cost. We address these shortcomings by introducing a Higher-order Projected Power Iteration method, which is (i) efficient and scales to tens of thousands of points, (ii) straightforward to implement, (iii) able to incorporate geometric consistency, (iv) guarantees cycle-consistent multi-matchings, and (iv) comes with theoretical convergence guarantees. Experimentally we show that our approach is superior to existing methods.

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