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Even Faster Algorithm for the Chamfer Distance

Authors Ying Feng, Piotr Indyk

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  • Theory of computation
Keywords
  • Chamfer distance

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Abstract

For two d-dimensional point sets A,B of size up to n, the Chamfer distance from A to B is defined as CH(A,B) = ∑_{a ∈ A} min_{b ∈ B} ‖a-b‖. The Chamfer distance is a widely used measure for quantifying dissimilarity between sets of points, used in many machine learning and computer vision applications. A recent work of Bakshi et al, NeuriPS'23, gave the first near-linear time (1+ε)-approximate algorithm, with a running time of 𝒪(nd log (n)/ε²). In this paper we improve the running time further, to 𝒪(nd(log log n+log1/(ε))/ε²)). When ε is a constant, this reduces the gap between the upper bound and the trivial Ω(dn) lower bound significantly, from 𝒪(log n) to 𝒪(log log n).

Cite As Get BibTex

Ying Feng and Piotr Indyk. Even Faster Algorithm for the Chamfer Distance. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 76:1-76:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.76

Author Details

Ying Feng
  • MIT, Cambridge, MA, USA
Piotr Indyk
  • MIT, Cambridge, MA, USA

Funding

  • Feng, Ying: Supported by an MIT Akamai Presidential Fellowship.
  • Indyk, Piotr: Supported in part by the NSF TRIPODS program (award DMS-2022448).

References

  1. Pdal: Chamfer. https://pdal.io/en/2.4.3/apps/chamfer.html, 2023. Accessed: 2023-05-12.
  2. Pytorch3d: Loss functions. https://pytorch3d.readthedocs.io/en/latest/modules/loss.html, 2023. Accessed: 2023-05-12.
  3. Tensorflow graphics: Chamfer distance. https://www.tensorflow.org/graphics/api_docs/python/tfg/nn/loss/chamfer_distance/evaluate, 2023. Accessed: 2023-05-12.
  4. Arne Andersson, Torben Hagerup, Stefan Nilsson, and Rajeev Raman. Sorting in linear time? In Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, STOC '95, pages 427-436, New York, NY, USA, 1995. Association for Computing Machinery. URL: https://doi.org/10.1145/225058.225173.
  5. Alexandr Andoni and Ilya Razenshteyn. Optimal data-dependent hashing for approximate near neighbors. In Proceedings of the forty-seventh annual ACM symposium on Theory of computing, pages 793-801, 2015. URL: https://doi.org/10.1145/2746539.2746553.
  6. Kubilay Atasu and Thomas Mittelholzer. Linear-complexity data-parallel earth mover’s distance approximations. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 364-373. PMLR, 09-15 June 2019. URL: https://proceedings.mlr.press/v97/atasu19a.html.
  7. Vassilis Athitsos and Stan Sclaroff. Estimating 3d hand pose from a cluttered image. In 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings., volume 2, pages II-432. IEEE, 2003. Google Scholar
  8. Ainesh Bakshi, Piotr Indyk, Rajesh Jayaram, Sandeep Silwal, and Erik Waingarten. A near-linear time algorithm for the chamfer distance, 2023. URL: https://doi.org/10.48550/arXiv.2307.03043.
  9. Manuel Blum, Robert W. Floyd, Vaughan Pratt, Ronald L. Rivest, and Robert E. Tarjan. Time bounds for selection. J. Comput. Syst. Sci., 7(4):448-461, August 1973. URL: https://doi.org/10.1016/S0022-0000(73)80033-9.
  10. Timothy M. Chan. Well-separated pair decomposition in linear time? Information Processing Letters, 107(5):138-141, 2008. URL: https://doi.org/10.1016/j.ipl.2008.02.008.
  11. Haoqiang Fan, Hao Su, and Leonidas J Guibas. A point set generation network for 3d object reconstruction from a single image. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 605-613, 2017. Google Scholar
  12. Sariel Har-Peled. Geometric approximation algorithms. Number 173. American Mathematical Soc., 2011. Google Scholar
  13. Piotr Indyk. Stable distributions, pseudorandom generators, embeddings, and data stream computation. Journal of the ACM (JACM), 53(3):307-323, 2006. URL: https://doi.org/10.1145/1147954.1147955.
  14. Li Jiang, Shaoshuai Shi, Xiaojuan Qi, and Jiaya Jia. Gal: Geometric adversarial loss for single-view 3d-object reconstruction. In Proceedings of the European conference on computer vision (ECCV), pages 802-816, 2018. Google Scholar
  15. Omar Khattab and Matei Zaharia. Colbert: Efficient and effective passage search via contextualized late interaction over bert. In Proceedings of the 43rd International ACM SIGIR conference on research and development in Information Retrieval, pages 39-48, 2020. URL: https://doi.org/10.1145/3397271.3401075.
  16. Jon M. Kleinberg. Two algorithms for nearest-neighbor search in high dimensions. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, STOC '97, pages 599-608, New York, NY, USA, 1997. Association for Computing Machinery. URL: https://doi.org/10.1145/258533.258653.
  17. Matt Kusner, Yu Sun, Nicholas Kolkin, and Kilian Weinberger. From word embeddings to document distances. In International conference on machine learning, pages 957-966. PMLR, 2015. URL: http://proceedings.mlr.press/v37/kusnerb15.html.
  18. Erik B Sudderth, Michael I Mandel, William T Freeman, and Alan S Willsky. Visual hand tracking using nonparametric belief propagation. In 2004 Conference on Computer Vision and Pattern Recognition Workshop, pages 189-189. IEEE, 2004. Google Scholar
  19. Ziyu Wan, Dongdong Chen, Yan Li, Xingguang Yan, Junge Zhang, Yizhou Yu, and Jing Liao. Transductive zero-shot learning with visual structure constraint. Advances in neural information processing systems, 32, 2019. Google Scholar
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