Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Robust affine point matching via quadratic assignment on Grassmannians (2303.02698v5)

Published 5 Mar 2023 in cs.CV

Abstract: Robust Affine Matching with Grassmannians (RoAM) is a new algorithm to perform affine registration of point clouds. The algorithm is based on minimizing the Frobenius distance between two elements of the Grassmannian. For this purpose, an indefinite relaxation of the Quadratic Assignment Problem (QAP) is used, and several approaches to affine feature matching are studied and compared. Experiments demonstrate that RoAM is more robust to noise and point discrepancy than previous methods.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (17)
  1. P. Barrios, V. Guzman, and M. Adams, “Pso-cola: A robust solution for correspondence-free point set registration,” in 2022 11th International Conference on Control, Automation and Information Sciences (ICCAIS).   IEEE, 2022, pp. 223–230.
  2. L. Tang, G. Hamarneh, and K. Iniewski, “Medical image registration: A review,” Medical imaging: technology and applications, vol. 1, pp. 619–660, 2013.
  3. P. Besl and N. D. McKay, “A method for registration of 3-D shapes,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239–256, 1992.
  4. X. Huang, G. Mei, J. Zhang, and R. Abbas, “A comprehensive survey on point cloud registration,” arXiv preprint arXiv:2103.02690, 2021.
  5. E. Begelfor and M. Werman, “Affine invariance revisited,” in 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’06), vol. 2, 2006, pp. 2087–2094.
  6. Y.-T. Chi, S. M. N. Shahed, J. Ho, and M.-H. Yang, “Higher dimensional affine registration and vision applications,” in Computer Vision – ECCV 2008, D. Forsyth, P. Torr, and A. Zisserman, Eds.   Berlin, Heidelberg: Springer Berlin Heidelberg, 2008, pp. 256–269.
  7. M. Moyou, A. Rangarajan, J. Corring, and A. M. Peter, “A grassmannian graph approach to affine invariant feature matching,” IEEE Transactions on Image Processing, vol. 29, pp. 3374–3387, 2020.
  8. V. Lyzinski, D. E. Fishkind, M. Fiori, J. T. Vogelstein, C. E. Priebe, and G. Sapiro, “Graph matching: Relax at your own risk,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 38, no. 1, pp. 60–73, 2016.
  9. T. C. Koopmans and M. Beckmann, “Assignment problems and the location of economic activities,” Econometrica: journal of the Econometric Society, pp. 53–76, 1957.
  10. J. T. Vogelstein, J. M. Conroy, V. Lyzinski, L. J. Podrazik, S. G. Kratzer, E. T. Harley, D. E. Fishkind, R. J. Vogelstein, and C. E. Priebe, “Fast approximate quadratic programming for graph matching,” PLOS ONE, vol. 10, no. 4, p. e0121002, 2015. [Online]. Available: https://doi.org/10.1371%2Fjournal.pone.0121002
  11. P.-Å. Wedin, “Perturbation bounds in connection with singular value decomposition,” BIT Numerical Mathematics, vol. 12, no. 1, pp. 99–111, 1972.
  12. G. W. Stewart, “Error and perturbation bounds for subspaces associated with certain eigenvalue problems,” SIAM Review, vol. 15, no. 4, pp. 727–764, 1973.
  13. S. Raghupathi, N. Brunhart-Lupo, and K. Gruchalla, “Caerbannog point clouds. National renewable energy laboratory,” https://data.nrel.gov/submissions/153, 2020.
  14. A. Kolpakov and M. Werman, “SageMath worksheets for RAG: Python code, numerical tests, and test statistics,” https://github.com/sashakolpakov/rag, 2023.
  15. The Sage Developers, “Sagemath, the Sage Mathematics Software System (Version 9.7.1),” 2022, https://www.sagemath.org.
  16. A. Kolpakov and M. Werman, “An approach to robust icp initialization,” IEEE Transactions on Pattern Analysis and Machine Intelligence, no. 01, pp. 1–9, jun 2023.
  17. O. Laric, “Three D Scans,” https://threedscans.com/, 2012.

Summary

We haven't generated a summary for this paper yet.