Representation LearningFree Access

eDiGS: Extended Divergence-Guided Shape Implicit Neural Representation for Unoriented Point Clouds

Yizhak Ben-Shabat

https://orcid.org/0000-0001-7547-7493

Technion Israel Institute of Technology, Faculty of Electrical and Computer Engineering, Haifa, Israel

E-mail Address: sitzikbs@gmail.com

Corresponding author.

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Chamin Hewa Koneputugodage

https://orcid.org/0009-0000-1333-5967

The Australian National University, College of Engineering, Computing and Cybernetics, Canberra, Australia

E-mail Address: chamin.hewa@anu.edu.au

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Stephen Gould

https://orcid.org/0000-0001-8929-7899

The Australian National University, College of Engineering, Computing and Cybernetics, Canberra, Australia

E-mail Address: tephen.gould@anu.edu.au

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https://doi.org/10.1142/S2811032324400046Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue on Towards Realistic 3D Deep Learning

Abstract

In this paper, we propose a new approach for learning shape implicit neural representations (INRs) from point cloud data that do not require normal vectors as input. We show that our method, which uses a soft constraint on the divergence of the distance function to the shape’s surface, can produce smooth solutions that accurately orient gradients to match the unknown normal at each point, even outperforming methods that use normal vectors directly. This work extends the latest work on divergence-guided sinusoidal activation INRs [Y. Ben-Shabat, C. H. Koneputugodage and S. Gould, Proc IEEE/CVF Conf Computer Vision and Pattern Recognition, 2022, pp. 19323–19332], to Gaussian activation INRs and provides extended theoretical analysis and results. We evaluate our approach on tasks related to surface reconstruction and shape space learning.

Keywords:

References

1. Y. Ben-Shabat, C. H. Koneputugodage and S. Gould, Proc IEEE/CVF Conf Computer Vision and Pattern Recognition, 2022, pp. 19323–19332. Google Scholar
2. J. J. Park, P. Florence, J. Straub, R. Newcombe and S. Lovegrove, CVPR, 2019, pp. 165–174. Google Scholar
3. L. Mescheder, M. Oechsle, M. Niemeyer, S. Nowozin and A. Geiger, CVPR, 2019, pp. 4460–4470. Google Scholar
4. S. Peng, M. Niemeyer, L. Mescheder, M. Pollefeys and A. Geiger, ECCV, 2020. Google Scholar
5. Z. Chen and H. Zhang, CVPR, 2019, pp. 5939–5948. Google Scholar
6. M. Atzmon and Y. Lipman, CVPR, 2020, pp. 2565–2574. Google Scholar
7. M. Atzmon and Y. Lipman, ICLR, 2021. Google Scholar
8. D. Urbach, Y. Ben-Shabat and M. Lindenbaum, ECCV, 2020, pp. 545–560. Google Scholar
9. A. Gropp, L. Yariv, N. Haim, M. Atzmon and Y. Lipman, ICML, Vol. 119, 2020, pp. 3789–3799, PMLR. Google Scholar
10. V. Sitzmann, J. Martel, A. Bergman, D. Lindell and G. Wetzstein, NeurIPS, Vol. 33, 2020. Google Scholar
11. S. Ramasinghe and S. Lucey, European Conf Computer Vision, 2022, pp. 142–158. Google Scholar
12. M. Berger, J. A. Levine, L. G. Nonato, G. Taubin and C. T. Silva, ACM Trans. Graphics, 2013, 32, 1–17. Crossref, Google Scholar
13. F. Bogo, J. Romero, G. Pons-Moll and M. J. Black, CVPR, 2017, pp. 6233–6242. Google Scholar
14. A. X. Chang et al., preprint, arXiv:1512.03012, 2015. Google Scholar
15. F. Cazals and J. Giesen, Effective Computational Geometry for Curves and Surfaces, Springer, 2006, pp. 231–276. Crossref, Google Scholar
16. R. Kolluri, J. R. Shewchuk and J. F. O’Brien, SGP, 2004, pp. 11–21. Crossref, Google Scholar
17. F. Bernardini, J. Mittleman, H. Rushmeier, C. Silva and G. Taubin, IEEE Trans. Visual. Comput. Graphics, 1999, 5, 349–359. Crossref, Google Scholar
18. N. Amenta, S. Choi and R. K. Kolluri, Comput. Geom., 2001, 19, 127–153. Crossref, Google Scholar
19. T. Groueix, M. Fisher, V. G. Kim, B. C. Russell and M. Aubry, CVPR, 2018, pp. 216–224. Google Scholar
20. F. Williams, T. Schneider, C. Silva, D. Zorin, J. Bruna and D. Panozzo, CVPR, 2019, pp. 10130–10139. Google Scholar
21. Y. Jiang, D. Ji, Z. Han and M. Zwicker, CVPR, 2020, pp. 1251–1261. Google Scholar
22. M. Tatarchenko, A. Dosovitskiy and T. Brox, ICCV, 2017, pp. 2088–2096. Google Scholar
23. S. Peng, C. Jiang, Y. Liao, M. Niemeyer, M. Pollefeys and A. Geiger, preprint, arXiv:2106.03452, 2021. Google Scholar
24. M. Berger, A. Tagliasacchi, L. M. Seversky, P. Alliez, G. Guennebaud, J. A. Levine, A. Sharf and C. T. Silva, Comput. Graphics Forum, 2017, 36, 301–329. Crossref, Google Scholar
25. M. Michalkiewicz, J. K. Pontes, D. Jack, M. Baktashmotlagh and A. Eriksson, ICCV, 2019, pp. 4743–4752. Google Scholar
26. M. Tancik, P. P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J. T. Barron and R. Ng, NeurIPS, 2020. Google Scholar
27. F. Williams, M. Trager, J. Bruna and D. Zorin, CVPR, 2021, pp. 9949–9958. Google Scholar
28. W. Yifan, L. Rahmann and O. Sorkine-Hornung, preprint, arXiv:2106.05187, 2021. Google Scholar
29. Y. Lipman, preprint, arXiv:2106.07689, 2021. Google Scholar
30. V. Sitzmann, M. Zollhöfer and G. Wetzstein, NeurIPS, 2019. Google Scholar
31. C. Jiang et al., CVPR, 2020, pp. 6001–6010. Google Scholar
32. D. Azinovic, R. Martin-Brualla, D. B. Goldman, M. Nießner and J. Thies, preprint, arXiv:2104.04532, 2021. Google Scholar
33. C. Williams and K. Duru, preprint, arXiv:2110.04957, 2021. Google Scholar
34. J. E. Marsden and A. Tromba, Vector Calculus, Macmillan, 2003. Google Scholar
35. P. M. Morse and H. Feshbach, Am. J. Phys., 1954, 22, 410–413. Crossref, Google Scholar
36. F. Cazals and M. Pouget, Comput. Aided Geom. Des., 2005, 22, 121–146. Crossref, Google Scholar
37. P. Guerrero, Y. Kleiman, M. Ovsjanikov and N. J. Mitra, Comput. Graphics Forum, 2018, 37, 75–85. Crossref, Google Scholar
38. Y. Ben-Shabat and S. Gould, ECCV, 2020, pp. 20–34. Google Scholar
39. Y. Ben-Shabat, M. Lindenbaum and A. Fischer, CVPR, 2019, pp. 10112–10120. Google Scholar
40. M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam and P. Vandergheynst, IEEE Signal Process. Mag., 2017, 34, 18–42. Crossref, Google Scholar
41. W. E. Lorensen and H. E. Cline, SIGGRAPH, Vol. 21, 1987, pp. 163–169, ACM, New York. Google Scholar
42. M. Kazhdan and H. Hoppe, ACM Trans. Graphics, 2013, 32, 1–13. Crossref, Google Scholar