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Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion

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Computer Vision – ECCV 2022 (ECCV 2022)

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Abstract

Explicit neural surface representations allow for exact and efficient extraction of the encoded surface at arbitrary precision, as well as analytic derivation of differential geometric properties such as surface normal and curvature. Such desirable properties, which are absent in its implicit counterpart, makes it ideal for various applications in computer vision, graphics and robotics. However, SOTA works are limited in terms of the topology it can effectively describe, distortion it introduces to reconstruct complex surfaces and model efficiency. In this work, we present Minimal Neural Atlas, a novel atlas-based explicit neural surface representation. At its core is a fully learnable parametric domain, given by an implicit probabilistic occupancy field defined on an open square of the parametric space. In contrast, prior works generally predefine the parametric domain. The added flexibility enables charts to admit arbitrary topology and boundary. Thus, our representation can learn a minimal atlas of 3 charts with distortion-minimal parameterization for surfaces of arbitrary topology, including closed and open surfaces with arbitrary connected components. Our experiments support the hypotheses and show that our reconstructions are more accurate in terms of the overall geometry, due to the separation of concerns on topology and geometry.

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References

  1. Atzmon, M., Lipman, Y.: SAL: sign agnostic learning of shapes from raw data. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2020)

    Google Scholar 

  2. Atzmon, M., Lipman, Y.: SALD: sign agnostic learning with derivatives. In: International Conference on Learning Representations (2021)

    Google Scholar 

  3. Badki, A., Gallo, O., Kautz, J., Sen, P.: Meshlet priors for 3d mesh reconstruction. In: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2020)

    Google Scholar 

  4. Baorui, M., Zhizhong, H., Yu-shen, L., Matthias, Z.: Neural-pull: learning signed distance functions from point clouds by learning to pull space onto surfaces. In: International Conference on Machine Learning (ICML) (2021)

    Google Scholar 

  5. Bednarik, J., Parashar, S., Gundogdu, E., Salzmann, M., Fua, P.: Shape reconstruction by learning differentiable surface representations. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2020)

    Google Scholar 

  6. Bekker, J., Davis, J.: Learning from positive and unlabeled data: a survey. Mach. Learn. 109, 719–760 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  7. Boulch, A., Langlois, P., Puy, G., Marlet, R.: NeeDrop: self-supervised shape representation from sparse point clouds using needle dropping. In: 2021 International Conference on 3D Vision (3DV) (2021)

    Google Scholar 

  8. Chang, A.X., et al.: ShapeNet: an information-rich 3D model repository. Technical report. arXiv:1512.03012 [cs.GR], Stanford University – Princeton University – Toyota Technological Institute at Chicago (2015)

  9. Chen, Z., Zhang, H.: Learning implicit fields for generative shape modeling. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    Google Scholar 

  10. Chibane, J., Mir, A., Pons-Moll, G.: Neural unsigned distance fields for implicit function learning. In: Advances in Neural Information Processing Systems (2020)

    Google Scholar 

  11. Cornea, O., Lupton, G., Oprea, J., Tanré, D.: Lusternik-Schnirelmann Category. American Mathematical Soc. (2003)

    Google Scholar 

  12. Degener, P., Meseth, J., Klein, R.: An adaptable surface parameterization method. In: IMR (2003)

    Google Scholar 

  13. Deng, Z., Bednarik, J., Salzmann, M., Fua, P.: Better patch stitching for parametric surface reconstruction. In: Proceedings - 2020 International Conference on 3D Vision, 3DV 2020 (2020)

    Google Scholar 

  14. Elkan, C., Noto, K.: Learning classifiers from only positive and unlabeled data. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2008)

    Google Scholar 

  15. Fan, H., Su, H., Guibas, L.: A point set generation network for 3d object reconstruction from a single image. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2017)

    Google Scholar 

  16. Fox, R.H.: On the Lusternik-Schnirelmann category. Ann. Math., 333–370 (1941)

    Google Scholar 

  17. Gropp, A., Yariv, L., Haim, N., Atzmon, M., Lipman, Y.: Implicit geometric regularization for learning shapes. In: International Conference on Machine Learning (2020)

    Google Scholar 

  18. Groueix, T., Fisher, M., Kim, V.G., Russell, B.C., Aubry, M.: A Papier-Mâché approach to learning 3D surface generation. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2018)

    Google Scholar 

  19. Gupta, K., Chandraker, M.: Neural mesh flow: 3D manifold mesh generation via diffeomorphic flows. In: Advances in Neural Information Processing Systems (2020)

    Google Scholar 

  20. Hormann, K., Greiner, G.: MIPS: an efficient global parametrization method, Technical report. Erlangen-Nuernberg Univ (Germany) Computer Graphics Group (2000)

    Google Scholar 

  21. James, I.: On category, in the sense of Lusternik-Schnirelmann. Topology 17, 331–348 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  22. Knapitsch, A., Park, J., Zhou, Q.Y., Koltun, V.: Tanks and temples: benchmarking large-scale scene reconstruction. ACM Trans. Graph. 36, 1–13 (2017)

    Article  Google Scholar 

  23. Madadi, M., Bertiche, H., Bouzouita, W., Guyon, I., Escalera, S.: Learning cloth dynamics: 3d + texture garment reconstruction benchmark. In: Proceedings of the NeurIPS 2020 Competition and Demonstration Track, PMLR (2021)

    Google Scholar 

  24. Mescheder, L., Oechsle, M., Niemeyer, M., Nowozin, S., Geiger, A.: Occupancy networks: learning 3d reconstruction in function space. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    Google Scholar 

  25. Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: NeRF: representing scenes as neural radiance fields for view synthesis. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) ECCV 2020. LNCS, vol. 12346, pp. 405–421. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58452-8_24

    Chapter  Google Scholar 

  26. Morreale, L., Aigerman, N., Kim, V., Mitra, N.J.: Neural surface maps. In: 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2021)

    Google Scholar 

  27. Pang, J., Li, D., Tian, D.: TearingNet: point cloud autoencoder to learn topology-friendly representations. In: 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2021)

    Google Scholar 

  28. Park, J.J., Florence, P., Straub, J., Newcombe, R., Lovegrove, S.: DeepSDF: learning continuous signed distance functions for shape representation. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    Google Scholar 

  29. Rabinovich, M., Poranne, R., Panozzo, D., Sorkine-Hornung, O.: Scalable locally injective mappings. ACM Trans. Graph. 36, 1 (2017)

    Article  Google Scholar 

  30. Schreiner, J., Asirvatham, A., Praun, E., Hoppe, H.: Inter-surface mapping. ACM Trans. Graph. 23, 870–877 (2004)

    Article  Google Scholar 

  31. Smith, J., Schaefer, S.: Bijective parameterization with free boundaries. ACM Trans. Graph 34, 1–9 (2015)

    Article  MATH  Google Scholar 

  32. Tatarchenko, M., Richter, S.R., Ranftl, R., Li, Z., Koltun, V., Brox, T.: What do single-view 3D reconstruction networks learn? In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2019)

    Google Scholar 

  33. Vaswani, A., et al.: Attention is all you need. In: Advances in Neural Information Processing Systems (2017)

    Google Scholar 

  34. Williams, F., Schneider, T., Silva, C., Zorin, D., Bruna, J., Panozzo, D.: Deep geometric prior for surface reconstruction. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2019)

    Google Scholar 

  35. Yang, Y., Feng, C., Shen, Y., Tian, D.: FoldingNet: point cloud auto-encoder via deep grid deformation. In: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2018)

    Google Scholar 

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Acknowledgements

This research/project is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-024), and the Tier 2 grant MOE-T2EP20120-0011 from the Singapore Ministry of Education.

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Correspondence to Weng Fei Low .

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Low, W.F., Lee, G.H. (2022). Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion. In: Avidan, S., Brostow, G., Cissé, M., Farinella, G.M., Hassner, T. (eds) Computer Vision – ECCV 2022. ECCV 2022. Lecture Notes in Computer Science, vol 13662. Springer, Cham. https://doi.org/10.1007/978-3-031-20086-1_27

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  • DOI: https://doi.org/10.1007/978-3-031-20086-1_27

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