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FastMAC: Stochastic Spectral Sampling of Correspondence Graph (2403.08770v1)

Published 13 Mar 2024 in cs.CV, cs.AI, and cs.RO

Abstract: 3D correspondence, i.e., a pair of 3D points, is a fundamental concept in computer vision. A set of 3D correspondences, when equipped with compatibility edges, forms a correspondence graph. This graph is a critical component in several state-of-the-art 3D point cloud registration approaches, e.g., the one based on maximal cliques (MAC). However, its properties have not been well understood. So we present the first study that introduces graph signal processing into the domain of correspondence graph. We exploit the generalized degree signal on correspondence graph and pursue sampling strategies that preserve high-frequency components of this signal. To address time-consuming singular value decomposition in deterministic sampling, we resort to a stochastic approximate sampling strategy. As such, the core of our method is the stochastic spectral sampling of correspondence graph. As an application, we build a complete 3D registration algorithm termed as FastMAC, that reaches real-time speed while leading to little to none performance drop. Through extensive experiments, we validate that FastMAC works for both indoor and outdoor benchmarks. For example, FastMAC can accelerate MAC by 80 times while maintaining high registration success rate on KITTI. Codes are publicly available at https://github.com/Forrest-110/FastMAC.

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References (76)
  1. Spinnet: Learning a general surface descriptor for 3d point cloud registration. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11753–11762, 2021.
  2. Pointdsc: Robust point cloud registration using deep spatial consistency. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15859–15869, 2021.
  3. Graph-cut ransac. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6733–6741, 2018.
  4. Globally optimal consensus set maximization through rotation search. In Computer Vision–ACCV 2012: 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part II 11, pages 539–551. Springer, 2013.
  5. Method for registration of 3-d shapes. In Sensor fusion IV: control paradigms and data structures, pages 586–606. Spie, 1992.
  6. Thomas M Breuel. Implementation techniques for geometric branch-and-bound matching methods. Computer Vision and Image Understanding, 90(3):258–294, 2003.
  7. Guaranteed outlier removal for point cloud registration with correspondences. IEEE transactions on pattern analysis and machine intelligence, 40(12):2868–2882, 2017.
  8. Representation granularity enables time-efficient autonomous exploration in large, complex worlds. Science Robotics, 8(80):eadf0970, 2023.
  9. Luca Carlone. Estimation contracts for outlier-robust geometric perception. arXiv preprint arXiv:2208.10521, 2022.
  10. Discrete signal processing on graphs: Sampling theory. IEEE transactions on signal processing, 63(24):6510–6523, 2015.
  11. Fast resampling of three-dimensional point clouds via graphs. IEEE Transactions on Signal Processing, 66(3):666–681, 2017.
  12. Pq-transformer: Jointly parsing 3d objects and layouts from point clouds. IEEE Robotics and Automation Letters, 7(2):2519–2526, 2022a.
  13. Sc2-pcr: A second order spatial compatibility for efficient and robust point cloud registration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13221–13231, 2022b.
  14. Robust euclidean alignment of 3d point sets: the trimmed iterative closest point algorithm. Image and vision computing, 23(3):299–309, 2005.
  15. The maximum consensus problem: recent algorithmic advances. Springer Nature, 2022.
  16. Robust fitting in computer vision: Easy or hard? In Proceedings of the European Conference on Computer Vision (ECCV), pages 701–716, 2018.
  17. Fully convolutional geometric features. In Proceedings of the IEEE/CVF international conference on computer vision, pages 8958–8966, 2019.
  18. Deep global registration. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2514–2523, 2020.
  19. Matching with prosac-progressive sample consensus. In 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05), pages 220–226. IEEE, 2005.
  20. A volumetric method for building complex models from range images. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 303–312, 1996.
  21. A comparison of volumetric information gain metrics for active 3d object reconstruction. Autonomous Robots, 42(2):197–208, 2018.
  22. Optimal correspondences from pairwise constraints. In 2009 IEEE 12th international conference on computer vision, pages 1295–1302. IEEE, 2009.
  23. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381–395, 1981.
  24. From semi-supervised to omni-supervised room layout estimation using point clouds. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 2803–2810. IEEE, 2023a.
  25. Dqs3d: Densely-matched quantization-aware semi-supervised 3d detection. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 21905–21915, 2023b.
  26. Are we ready for autonomous driving? the kitti vision benchmark suite. In 2012 IEEE conference on computer vision and pattern recognition, pages 3354–3361. IEEE, 2012.
  27. Multi-scale em-icp: A fast and robust approach for surface registration. In Computer Vision—ECCV 2002: 7th European Conference on Computer Vision Copenhagen, Denmark, May 28–31, 2002 Proceedings, Part IV 7, pages 418–432. Springer, 2002.
  28. Global optimization through rotation space search. International Journal of Computer Vision, 82(1):64–79, 2009.
  29. Fast svd for large-scale matrices. In Workshop on Efficient Machine Learning at NIPS, pages 249–252, 2007.
  30. Predator: Registration of 3d point clouds with low overlap. In Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition, pages 4267–4276, 2021.
  31. Robust matching of 3d contours using iterative closest point algorithm improved by m-estimation. Pattern Recognition, 36(9):2041–2047, 2003.
  32. Amlesac: A new maximum likelihood robust estimator. Proc. of Graphicon-2005. Novosibirsk, pages 93–100, 2005.
  33. A spectral technique for correspondence problems using pairwise constraints. In Tenth IEEE International Conference on Computer Vision (ICCV’05) Volume 1, pages 1482–1489. IEEE, 2005.
  34. Hongdong Li. Consensus set maximization with guaranteed global optimality for robust geometry estimation. In 2009 IEEE 12th International Conference on Computer Vision, pages 1074–1080. IEEE, 2009.
  35. Lode: Locally conditioned eikonal implicit scene completion from sparse lidar. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 8269–8276. IEEE, 2023.
  36. K-closest points and maximum clique pruning for efficient and effective 3-d laser scan matching. IEEE Robotics and Automation Letters, 7(2):1471–1477, 2022.
  37. Sift flow: Dense correspondence across scenes and its applications. IEEE transactions on pattern analysis and machine intelligence, 33(5):978–994, 2010.
  38. Clipper: A graph-theoretic framework for robust data association. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 13828–13834. IEEE, 2021.
  39. Convergent iterative closest-point algorithm to accomodate anisotropic and inhomogenous localization error. IEEE transactions on pattern analysis and machine intelligence, 34(8):1520–1532, 2011.
  40. Pairwise consistent measurement set maximization for robust multi-robot map merging. In 2018 IEEE international conference on robotics and automation (ICRA), pages 2916–2923. IEEE, 2018.
  41. Emerging topics in computer vision. Prentice Hall PTR, 2004.
  42. Active visuo-tactile interactive robotic perception for accurate object pose estimation in dense clutter. IEEE Robotics and Automation Letters, 7(2):4686–4693, 2022.
  43. Branch-and-bound methods for euclidean registration problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(5):783–794, 2008.
  44. 3dregnet: A deep neural network for 3d point registration. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 7193–7203, 2020.
  45. The complexity of the matrix eigenproblem. In Proceedings of the thirty-first annual ACM symposium on Theory of computing, pages 507–516, 1999.
  46. A practical maximum clique algorithm for matching with pairwise constraints. arXiv preprint arXiv:1902.01534, 2019.
  47. Comparing icp variants on real-world data sets: Open-source library and experimental protocol. Autonomous robots, 34:133–148, 2013.
  48. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 652–660, 2017.
  49. Geometric transformer for fast and robust point cloud registration. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11143–11152, 2022.
  50. Compatibility-guided sampling consensus for 3-d point cloud registration. IEEE Transactions on Geoscience and Remote Sensing, 58(10):7380–7392, 2020.
  51. Fast point feature histograms (fpfh) for 3d registration. In 2009 IEEE international conference on robotics and automation, pages 3212–3217. IEEE, 2009.
  52. Big data analysis with signal processing on graphs: Representation and processing of massive data sets with irregular structure. IEEE signal processing magazine, 31(5):80–90, 2014a.
  53. Discrete signal processing on graphs: Frequency analysis. IEEE Transactions on Signal Processing, 62(12):3042–3054, 2014b.
  54. Generalized-icp. In Robotics: science and systems, page 435. Seattle, WA, 2009.
  55. Robin: a graph-theoretic approach to reject outliers in robust estimation using invariants. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 13820–13827. IEEE, 2021.
  56. Scene coordinate regression forests for camera relocalization in rgb-d images. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2930–2937, 2013.
  57. Consensus maximization with linear matrix inequality constraints. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4941–4949, 2017.
  58. Lei Sun. Ransic: Fast and highly robust estimation for rotation search and point cloud registration using invariant compatibility. IEEE Robotics and Automation Letters, 7(1):143–150, 2021.
  59. Raft-3d: Scene flow using rigid-motion embeddings. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8375–8384, 2021.
  60. Vibus: Data-efficient 3d scene parsing with viewpoint bottleneck and uncertainty-spectrum modeling. ISPRS Journal of Photogrammetry and Remote Sensing, 194:302–318, 2022.
  61. Guided sampling and consensus for motion estimation. In Computer Vision—ECCV 2002: 7th European Conference on Computer Vision Copenhagen, Denmark, May 28–31, 2002 Proceedings, Part I 7, pages 82–96. Springer, 2002.
  62. Philip H. S. Torr. Bayesian model estimation and selection for epipolar geometry and generic manifold fitting. International Journal of Computer Vision, 50:35–61, 2002.
  63. Duncan J Watts. Networks, dynamics, and the small-world phenomenon. American Journal of sociology, 105(2):493–527, 1999.
  64. Sc-wls: Towards interpretable feed-forward camera re-localization. In European Conference on Computer Vision, pages 585–601. Springer, 2022.
  65. Graduated non-convexity for robust spatial perception: From non-minimal solvers to global outlier rejection. IEEE Robotics and Automation Letters, 5(2):1127–1134, 2020a.
  66. Teaser: Fast and certifiable point cloud registration. IEEE Transactions on Robotics, 37(2):314–333, 2020b.
  67. Go-icp: A globally optimal solution to 3d icp point-set registration. IEEE transactions on pattern analysis and machine intelligence, 38(11):2241–2254, 2015.
  68. Sac-cot: Sample consensus by sampling compatibility triangles in graphs for 3-d point cloud registration. IEEE Transactions on Geoscience and Remote Sensing, 60:1–15, 2021.
  69. Cofinet: Reliable coarse-to-fine correspondences for robust pointcloud registration. Advances in Neural Information Processing Systems, 34:23872–23884, 2021.
  70. 3dmatch: Learning local geometric descriptors from rgb-d reconstructions. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1802–1811, 2017.
  71. 3d registration with maximal cliques. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17745–17754, 2023.
  72. Zhengyou Zhang. Iterative point matching for registration of free-form curves and surfaces. International journal of computer vision, 13(2):119–152, 1994.
  73. Deterministically maximizing feasible subsystem for robust model fitting with unit norm constraint. In CVPR 2011, pages 1825–1832. IEEE, 2011.
  74. Snake: Shape-aware neural 3d keypoint field. Advances in Neural Information Processing Systems, 35:7052–7064, 2022.
  75. 3d implicit transporter for temporally consistent keypoint discovery. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3869–3880, 2023.
  76. Fast global registration. In Computer Vision–ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part II 14, pages 766–782. Springer, 2016.
Citations (5)
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Summary

  • The paper presents FastMAC, which applies graph signal processing with high-pass filtering to efficiently accelerate maximal clique search in 3D registration.
  • It leverages stochastic spectral sampling to pinpoint high-frequency nodes, significantly reducing computational cost while preserving registration accuracy.
  • Empirical results on the KITTI dataset demonstrate an 80-fold acceleration compared to traditional methods, underscoring its potential for real-time applications.

Stochastic Spectral Sampling Enhances 3D Point Cloud Registration with FastMAC

Introduction

3D correspondence graph, a fundamental structure in computer vision, encapsulates vital information for 3D point cloud registration by defining compatibility edges between pairs of 3D points. Despite its significance, especially in maximal clique search-based methods like MAC, the underlying properties and potential optimization of correspondence graphs have not been fully explored. This paper introduces a novel perspective by employing graph signal processing to analyze and sample correspondence graphs, proposing FastMAC—a stochastic spectral sampling framework which enables notably faster 3D registration with minimal impact on performance.

Graph Signal Processing and FastMAC

The core contribution of this paper is the application of graph signal processing to the domain of 3D correspondence graphs. By defining a signal based on the generalized degree of nodes in the graph, the paper explores the spectral domain to identify and sample high-frequency nodes. This approach is grounded in the understanding that high-frequency nodes, characterized by rapid changes in their generalized degree, are critical for successful maximal clique search—a central process in many state-of-the-art 3D registration algorithms.

FastMAC operationalizes this insight through a stochastic spectral sampling strategy that prioritizes nodes based on their response to a high-pass graph filter. The high-pass filter is designed to accentuate features of the graph signal that represent rapid variations, thus identifying nodes that are likely to be pivotal in forming maximal cliques. The stochastic nature of the sampling process, informed by the nodes' response magnitudes, ensures efficiency and avoids the computational burdens associated with deterministic methods.

Empirical Validation

Extensive experiments substantiate the efficacy of FastMAC across diverse benchmarks. Notably, on the KITTI dataset, FastMAC achieves an 80-fold acceleration of the MAC algorithm while maintaining a high registration success rate. These results are promising, indicating that FastMAC can facilitate real-time 3D registration without significant sacrifices in accuracy.

The comparison of sampling strategies further reinforces the superiority of the proposed method. FastMAC consistently outperforms traditional sampling techniques, such as random sampling and farthest point sampling, across various metrics and datasets. This performance highlights the benefits of a spectral approach to graph sampling in the context of 3D registration.

Implications and Future Directions

The introduction of FastMAC represents a significant step forward in the exploration of 3D correspondence graphs through the lens of graph signal processing. By efficiently identifying and leveraging high-frequency nodes, FastMAC opens new avenues for optimizing 3D registration processes.

Looking ahead, the principles underpinning FastMAC could inspire further research into real-time applications of 3D registration, such as SLAM and 3D reconstruction. Moreover, the potential for integrating learning-based methods with spectral graph sampling poses an intriguing direction for future work, potentially enabling even more effective and adaptive solutions to 3D registration challenges.

In conclusion, the development of FastMAC marks a notable advancement in the quest for efficient and accurate 3D point cloud registration. By harnessing the insights of graph signal processing in a novel and practical framework, this work sets the stage for a new era of exploration and innovation in the field of computer vision.

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