Abstract
Recent advances in radiance fields enable photorealistic rendering of static or dynamic 3D scenes, but still do not support explicit deformation that is used for scene manipulation or animation. In this paper, we propose a method that enables a new type of deformation of the radiance field: free-form radiance field deformation. We use a triangular mesh that encloses the foreground object called cage as an interface, and by manipulating the cage vertices, our approach enables the free-form deformation of the radiance field. The core of our approach is cage-based deformation which is commonly used in mesh deformation. We propose a novel formulation to extend it to the radiance field, which maps the position and the view direction of the sampling points from the deformed space to the canonical space, thus enabling the rendering of the deformed scene. The deformation results of the synthetic datasets and the real-world datasets demonstrate the effectiveness of our approach. Project page: https://xth430.github.io/deforming-nerf/.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
In fact, the actual number is smaller than this approximation since we only compute for points inside the cage.
References
Barron, J.T., Mildenhall, B., Tancik, M., Hedman, P., Martin-Brualla, R., Srinivasan, P.P.: Mip-NeRF: a multiscale representation for anti-aliasing neural radiance fields. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 5855–5864 (2021)
Chen, A., Xu, Z., Geiger, A., Yu, J., Su, H.: TensoRF: tensorial radiance fields. In: European Conference on Computer Vision (2022)
Community, B.O.: Blender - a 3D modelling and rendering package. Blender Foundation, Stichting Blender Foundation, Amsterdam (2018). http://www.blender.org
Davis, A., Levoy, M., Durand, F.: Unstructured light fields. In: Computer Graphics Forum, vol. 31, pp. 305–314. Wiley Online Library (2012)
DeRose, T., Meyer, M.: Harmonic coordinates. In: Pixar Technical Memo 06–02. Pixar Animation Studios (2006)
Fan, H., Su, H., Guibas, L.J.: 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, pp. 605–613 (2017)
Floater, M.S.: Mean value coordinates. Comput. Aided Geom. Des. 20, 19–27 (2003)
Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: radiance fields without neural networks. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5501–5510 (2022)
Girdhar, R., Fouhey, D.F., Rodriguez, M., Gupta, A.: Learning a predictable and generative vector representation for objects. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9910, pp. 484–499. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46466-4_29
Gortler, S.J., Grzeszczuk, R., Szeliski, R., Cohen, M.F.: The Lumigraph. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 43–54 (1996)
Guo, M.H., Cai, J.X., Liu, Z.N., Mu, T.J., Martin, R.R., Hu, S.M.: PCT: point cloud transformer. Comput. Vis. Media 7, 187–199 (2021)
Guo, M., Fathi, A., Wu, J., Funkhouser, T.: Object-centric neural scene rendering. arXiv preprint arXiv:2012.08503 (2020)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)
Jakab, T., Tucker, R., Makadia, A., Wu, J., Snavely, N., Kanazawa, A.: KeypointDeformer: unsupervised 3d Keypoint discovery for shape control. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 12783–12792 (2021)
Jensen, R., Dahl, A., Vogiatzis, G., Tola, E., Aanæs, H.: Large scale multi-view stereopsis evaluation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 406–413 (2014)
Jiakai, Z., et al.: Editable free-viewpoint video using a layered neural representation. In: ACM SIGGRAPH (2021)
Joshi, P., Meyer, M., DeRose, T., Green, B., Sanocki, T.: Harmonic coordinates for character articulation. ACM Trans. Graph. (TOG) 26, 71-es (2007)
Ju, T., Schaefer, S., Warren, J.: Mean value coordinates for closed triangular meshes. In: ACM SIGGRAPH 2005 Papers, pp. 561–566 (2005)
Kajiya, J.T., Von Herzen, B.P.: Ray tracing volume densities. ACM SIGGRAPH Comput. Graph. 18, 165–174 (1984)
Kanazawa, A., Tulsiani, S., Efros, A.A., Malik, J.: Learning category-specific mesh reconstruction from image collections. In: Ferrari, V., Hebert, M., Sminchisescu, C., Weiss, Y. (eds.) ECCV 2018. LNCS, vol. 11219, pp. 386–402. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01267-0_23
Kato, H., Ushiku, Y., Harada, T.: Neural 3D mesh renderer. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3907–3916 (2018)
Lipman, Y., Levin, D., Cohen-Or, D.: Green coordinates. ACM Trans. Graph. (TOG) 27, 1–10 (2008)
Liu, L., Gu, J., Zaw Lin, K., Chua, T.S., Theobalt, C.: Neural sparse voxel fields. In: Advances in Neural Information Processing Systems, vol. 33, pp. 15651–15663 (2020)
Liu, L., Habermann, M., Rudnev, V., Sarkar, K., Gu, J., Theobalt, C.: Neural actor: neural free-view synthesis of human actors with pose control. ACM Trans. Graph. (ACM SIGGRAPH Asia) 40, 1–16 (2021)
Liu, S., Zhang, X., Zhang, Z., Zhang, R., Zhu, J.Y., Russell, B.: Editing conditional radiance fields. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 5773–5783 (2021)
Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. ACM SIGGRAPH Comput. Graph. 21, 163–169 (1987)
Mildenhall, B., Hedman, P., Martin-Brualla, R., Srinivasan, P.P., Barron, J.T.: NeRF in the dark: high dynamic range view synthesis from noisy raw images. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 16190–16199 (2022)
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
Müller, T., Evans, A., Schied, C., Keller, A.: Instant neural graphics primitives with a multiresolution hash encoding. ACM Trans. Graph 41, 1–15 (2022)
Niemeyer, M., Mescheder, L., Oechsle, M., Geiger, A.: Differentiable volumetric rendering: learning implicit 3D representations without 3D supervision. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3504–3515 (2020)
Nieto, J.R., Susín, A.: Cage based deformations: a survey. In: González Hidalgo, M., Mir Torres, A., Varona Gómez, J. (eds.) Deformation Models, vol. 7, pp. 75–99. Springer, Dordrecht (2013). https://doi.org/10.1007/978-94-007-5446-1_3
Noguchi, A., Iqbal, U., Tremblay, J., Harada, T., Gallo, O.: Watch it move: unsupervised discovery of 3d joints for re-posing of articulated objects. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3677–3687 (2022)
Noguchi, A., Sun, X., Lin, S., Harada, T.: Neural articulated radiance field. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 5762–5772 (2021)
Ost, J., Mannan, F., Thuerey, N., Knodt, J., Heide, F.: Neural scene graphs for dynamic scenes. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 2856–2865 (2021)
Park, K., et al.: Nerfies: deformable neural radiance fields. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 5865–5874 (2021)
Park, K., et al.: HyperNeRF: a higher-dimensional representation for topologically varying neural radiance fields. ACM Trans. Graph 40, 1–12 (2021)
Peng, S., et al.: Animatable neural radiance fields for modeling dynamic human bodies. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 14314–14323 (2021)
Peng, S., et al.: Neural body: implicit neural representations with structured latent codes for novel view synthesis of dynamic humans. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9054–9063 (2021)
Pumarola, A., Corona, E., Pons-Moll, G., Moreno-Noguer, F.: D-NeRF: neural radiance fields for dynamic scenes. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10318–10327 (2021)
Sitzmann, V., Zollhöfer, M., Wetzstein, G.: Scene representation networks: continuous 3D-structure-aware neural scene representations. In: Advances in Neural Information Processing Systems, vol. 32 (2019)
Su, S.Y., Yu, F., Zollhöfer, M., Rhodin, H.: A-NeRF: articulated neural radiance fields for learning human shape, appearance, and pose. In: Advances in Neural Information Processing Systems, vol. 34, 12278–12291 (2021)
Sun, C., Sun, M., Chen, H.T.: Direct voxel grid optimization: super-fast convergence for radiance fields reconstruction. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5459–5469 (2022)
Tretschk, E., Tewari, A., Golyanik, V., Zollhöfer, M., Lassner, C., Theobalt, C.: Non-rigid neural radiance fields: reconstruction and novel view synthesis of a dynamic scene from monocular video. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 12959–12970 (2021)
Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment—a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) IWVA 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44480-7_21
Xian, C., Lin, H., Gao, S.: Automatic generation of coarse bounding cages from dense meshes. In: IEEE International Conference on Shape Modeling and Applications (2009)
Xu, T., Fujita, Y., Matsumoto, E.: Surface-aligned neural radiance fields for controllable 3D human synthesis. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 15883–15892 (2022)
Yan, X., Yang, J., Yumer, E., Guo, Y., Lee, H.: Perspective transformer nets: learning single-view 3D object reconstruction without 3D supervision. In: Advances in Neural Information Processing Systems, vol. 29 (2016)
Yang, B., et al.: Learning object-compositional neural radiance field for editable scene rendering. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 13779–13788 (2021)
Yifan, W., Aigerman, N., Kim, V.G., Chaudhuri, S., Sorkine-Hornung, O.: Neural cages for detail-preserving 3D deformations. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 75–83 (2020)
Yuan, Y.J., Sun, Y.T., Lai, Y.K., Ma, Y., Jia, R., Gao, L.: NeRF-Editing: geometry editing of neural radiance fields. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 18353–18364 (2022)
Acknowledgements
We would like to thank Daisuke Kasuga, Ryosuke Sasaki, Tomoyuki Takahata, Haruo Fujiwara, and Atsuhiro Noguchi for comments and discussions. This work was partially supported by JST AIP Acceleration Research JPMJCR20U3, Moonshot R &D Grant Number JPMJPS2011, CREST Grant Number JPMJCR2015, JSPS KAKENHI Grant Number JP19H01115 and Basic Research Grant (Super AI) of Institute for AI and Beyond of the University of Tokyo.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Xu, T., Harada, T. (2022). Deforming Radiance Fields with Cages. 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 13693. Springer, Cham. https://doi.org/10.1007/978-3-031-19827-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-031-19827-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-19826-7
Online ISBN: 978-3-031-19827-4
eBook Packages: Computer ScienceComputer Science (R0)