Provably Approximated Point Cloud Registration

Jubran, Ibrahim; Maalouf, Alaa; Kimmel, Ron; Feldman, Dan

doi:10.1109/iccv48922.2021.01302

Cited by 8 publications

(6 citation statements)

References 41 publications

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“…In Figure 1 we see a numerical verification of this result. We further see that in practice most other methods also obtain energy which is lower than √ 2E 2 (A * ), with the exception of the algorithm of [22] in high dimensions.…”

Section: Demonstration Of Theoretical Resultsmentioning

confidence: 79%

“…Besides the Approx-Alignment (AA) algorithm of [22], methods plotted in Figure 1 are the standard Rigid Procrustes (1) (Procrustes); the non-symmetrized relaxation of (2), min…”

Section: Demonstration Of Theoretical Resultsmentioning

confidence: 99%

“…Our numerical experiments, presented in Section 4, show that our method for the robust Procrustes problem has practical advantages. In comparison to [22], the only method known to us with theoretical approximation guarantees, our method performs better in high dimensions. This is in accordance with the fact that our approximation factor is a constant and does not depend on d, whereas their factor grows exponentially with d. Although having no theoretical guarantees, an IRLS approach performs on par or better than both our method and that of Jubran et al Typically initializing IRLS with the solution of our method leads to similar results, but leads to significantly improved results in certain settings; see Figure 3.…”

Section: Introductionmentioning

confidence: 94%

“…While this method often works well in practice, it may fail find a global minimizer since (in contrast with more classical IRLS applications [21]) the domain of ( 2) is non-convex. In fact, it seems that there were no known algorithms with theoretical guarantees for this problem until the recent paper [22], where a RANSAC-like algorithm was proposed. Given enough running time, this algorithm was shown to find a solution whose energy is optimal up to a multiplicative constant (1 + √ 2) d which depends exponentially on d. While in practice this algorithm works well for low-dimensional problems, its performance deteriorates as the dimension increases, which is common to RANSAC-type algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Symmetrized Robust Procrustes: Constant-Factor Approximation and Exact Recovery

Amir¹,

Kovalsky²,

Dym³

2022

Preprint

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The classical Procrustes problem is to find a rigid motion (orthogonal transformation and translation) that best aligns two given point-sets in the least-squares sense. The Robust Procrustes problem is an important variant, in which a power-1 objective is used instead of least squares to improve robustness to outliers. While the optimal solution of the least-squares problem can be easily computed in closed form, dating back to Schönemann (1966), no such solution is known for the power-1 problem. In this paper we propose a novel convex relaxation for the Robust Procrustes problem. Our relaxation enjoys several theoretical and practical advantages: Theoretically, we prove that our method provides a √ 2-factor approximation to the Robust Procrustes problem, and that, under appropriate assumptions, it exactly recovers the true rigid motion from point correspondences contaminated by outliers. In practice, we find in numerical experiments on both synthetic and real robust Procrustes problems, that our method performs similarly to the standard Iteratively Reweighted Least Squares (IRLS). However the convexity of our algorithm allows incorporating additional convex penalties, which are not readily amenable to IRLS. This turns out to be a substantial advantage, leading to improved results in high-dimensional problems, including non-rigid shape alignment and semi-supervised interlingual word translation.Preprint. Under review.

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Section: Demonstration Of Theoretical Resultsmentioning

confidence: 79%

“…Besides the Approx-Alignment (AA) algorithm of [22], methods plotted in Figure 1 are the standard Rigid Procrustes (1) (Procrustes); the non-symmetrized relaxation of (2), min…”

Section: Demonstration Of Theoretical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Symmetrized Robust Procrustes: Constant-Factor Approximation and Exact Recovery

Amir¹,

Kovalsky²,

Dym³

2022

Preprint

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“…It can be observed that among conventional optimization methods, RANSAC [32], ICP [8], and its variants like TrICP [9], CICP [10], PICP [33], and Super4PCS [13], do not show significant advantages in recall rate and estimation error. The graph matching-based GCTR [18] has an even lower recall rate, while methods based on Gaussian Mixture Model (GMM), such as FilterReg [15], demonstrate relatively better recall rates and moderate estimation errors.…”

Section: Performancementioning

confidence: 99%

Point Cloud Registration Based on Global and Local Feature Fusion

Yue

Yuan

et al. 2022

IFIP Advances in Information and Communication Technology

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Cross-modality point cloud registration is confronted with significant challenges due to inherent differences in modalities between different sensors. We propose a cross-modality point cloud registration framework FF-LOGO: a cross-modality point cloud registration method with feature filtering and local-global optimization. The crossmodality feature correlation filtering module extracts geometric transformation-invariant features from cross-modality point clouds and achieves point selection by feature matching. We also introduce a cross-modality optimization process, including a local adaptive key region aggregation module and a global modality consistency fusion optimization module. Experimental results demonstrate that our two-stage optimization significantly improves the registration accuracy of the feature association and selection module. Our method achieves a substantial increase in recall rate compared to the current state-of-the-art methods on the 3DCSR dataset, improving from 40.59% to 75.74%. Our code will be available at https://github.com/wangmohan17/FFLOGO.

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