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Soft Shadow Diffusion (SSD): Physics-Inspired Learning for 3D Computational Periscopy

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Computer Vision – ECCV 2024 (ECCV 2024)

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Abstract

Conventional imaging requires a line of sight to create accurate visual representations of a scene. In certain circumstances, however, obtaining a suitable line of sight may be impractical, dangerous, or even impossible. Non-line-of-sight (NLOS) imaging addresses this challenge by reconstructing the scene from indirect measurements. Recently, passive NLOS methods that use an ordinary photograph of the subtle shadow cast onto a visible wall by the hidden scene have gained interest. These methods are currently limited to 1D or low-resolution 2D color imaging or to localizing a hidden object whose shape is approximately known. Here, we generalize this class of methods and demonstrate a 3D reconstruction of a hidden scene from an ordinary NLOS photograph. To achieve this, we propose a novel reformulation of the light transport model that conveniently decomposes the hidden scene into light-occluding and non-light-occluding components to yield a separable non-linear least squares (SNLLS) inverse problem. We develop two solutions: A gradient-based optimization method and a physics-inspired neural network approach, which we call Soft Shadow diffusion (SSD). Despite the challenging ill-conditioned inverse problem encountered here, our approaches are effective on numerous 3D scenes in real experimental scenarios. Moreover, SSD is trained in simulation but generalizes well to unseen classes in simulation and real-world NLOS scenes. SSD also shows surprising robustness to noise and ambient illumination.

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References

  1. Adib, F., Katabi, D.: See through walls with wifi! In: Proc. ACM SIGCOMM, p. 75–86 (2013)

    Google Scholar 

  2. Aittala, M., et al.: Computational mirrors: Blind inverse light transport by deep matrix factorization. Advances in Neural Information Processing Systems (NeurIPS) 32 (2019)

    Google Scholar 

  3. Baradad, M., et al.: Inferring light fields from shadows. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 6267–6275 (2018)

    Google Scholar 

  4. Boger-Lombard, J., Slobodkin, Y., Katz, O.: Towards passive non-line-of-sight acoustic localization around corners using uncontrolled random noise sources. Sci. Rep. 13(1), 4952 (2023)

    Article  Google Scholar 

  5. Bouman, K.L., et al.: Turning corners into cameras: principles and methods. In: Proc. IEEE/CVF Int. Conf. Computer Vision (ICCV), October 2017

    Google Scholar 

  6. Cai, R., Lai, H., Chami, I., Guibas, L.J.: Learning gradient fields for shape generation. In: Proc. Eur. Conf. Computer Vision (ECCV), pp. 10751–10760 (2020)

    Google Scholar 

  7. Cavanagh, P., Leclerc, Y.G.: Shape from shadows. J. Exp. Psychol. Hum. Percept. Perform. 15(1), 3 (1989)

    Article  Google Scholar 

  8. Chang, A.X., et al.: Shapenet: an information-rich 3d model repository (2015)

    Google Scholar 

  9. Chaudhury, A.N., Keselman, L., Atkeson, C.G.: Shape from shading for robotic manipulation. In: Proc. IEEE/CVF Winter Conf. on Applications of Computer Vision (WACV), pp. 8389–8398. IEEE (2024)

    Google Scholar 

  10. Chou, G., Bahat, Y., Heide, F.: Diffusion-sdf: conditional generative modeling of signed distance functions. In: Proc. IEEE/CVF Int. Conf. Computer Vision (ICCV) (2023)

    Google Scholar 

  11. Cohen, A.L.: Anti-pinhole imaging. Opt. Acta 29(1), 63–67 (1982)

    Article  Google Scholar 

  12. Community, B.O.: Blender - a 3D modelling and rendering package. Blender Foundation, Stichting Blender Foundation, Amsterdam (2018). http://www.blender.org

  13. Czajkowski, R., Murray-Bruce, J.: Two-edge-resolved three-dimensional non-line-of-sight imaging with an ordinary camera. Nat. Commun. 15(1162) (2024)

    Google Scholar 

  14. Dhariwal, P., Nichol, A.: Diffusion models beat gans on image synthesis. In: Advances in Neural Information Processing Systems (NeurIPS) (2021)

    Google Scholar 

  15. Faccio, D., Velten, A., Wetzstein, G.: Non-line-of-sight imaging. Nature Rev. Phys. 2(6), 318–327 (2020)

    Article  Google Scholar 

  16. Geng, R., et al.: Passive non-line-of-sight imaging using optimal transport. IEEE Trans. Image Process. 31, 110–124 (2022)

    Article  Google Scholar 

  17. Heide, F., O’Toole, M., Zang, K., Lindell, D.B., Diamond, S., Wetzstein, G.: Non-line-of-sight imaging with partial occluders and surface normals. ACM Trans. Graph. (2019)

    Google Scholar 

  18. Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. In: Advances in Neural Information Processing Systems (NeurIPS), vol. 33, pp. 6840–6851 (2020)

    Google Scholar 

  19. Horn, B.K.P., Brooks, M.J. (eds.): Shape from Shading. MIT Press, Cambridge (1989)

    Google Scholar 

  20. Iwashita, Y., Stoica, A., Kurazume, R.: Gait identification using shadow biometrics. Pattern Recogn. Lett. 33(16), 2148–2155 (2012)

    Article  Google Scholar 

  21. Jain, A., Mildenhall, B., Barron, J.T., Abbeel, P., Poole, B.: Zero-shot text-guided object generation with dream fields. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), December 2021

    Google Scholar 

  22. Kaga, M., Kushida, T., Takatani, T., Tanaka, K., Funatomi, T., Mukaigawa, Y.: Thermal non-line-of-sight imaging from specular and diffuse reflections. IPSJ Trans. Comput. Vision Appl. 11 (12 2019)

    Google Scholar 

  23. Karnieli, A., Fried, O., Hel-Or, Y.: Deepshadow: neural shape from shadow. In: Proc. Eur. Conf. Computer Vision (ECCV), pp. 415–430 (2022)

    Google Scholar 

  24. Khalid, N.M., Xie, T., Belilovsky, E., Tiberiu, P.: Clip-mesh: generating textured meshes from text using pretrained image-text models. In: SIGGRAPH Asia 2022 Conference Papers, December 2022

    Google Scholar 

  25. Kirmani, A., Jeelani, H., Montazerhodjat, V., Goyal, V.K.: Diffuse imaging: creating optical images with unfocused time-resolved illumination and sensing. IEEE Signal Process. Lett. 19(1), 31–34 (2012)

    Article  Google Scholar 

  26. Kong, Z., Ping, W., Huang, J., Zhao, K., Catanzaro, B.: Diffwave: a versatile diffusion model for audio synthesis. In: Proc. Int. Conf. on Learning Representations (ICLR) (2021)

    Google Scholar 

  27. gil Lee, S., et al.: Priorgrad: improving conditional denoising diffusion models with data-dependent adaptive prior. In: Proc. Int. Conf. on Learning Representations (ICLR) (2022)

    Google Scholar 

  28. Lindell, D.B., Wetzstein, G., Koltun, V.: Acoustic non-line-of-sight imaging. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 6773–6782 (2019)

    Google Scholar 

  29. Lindell, D.B., Wetzstein, G., O’Toole, M.: Wave-based non-line-of-sight imaging using fast fk migration. ACM Trans. Graphics 38(4), 1–13 (2019)

    Article  Google Scholar 

  30. Ling, J., Wang, Z., Xu, F.: Shadowneus: neural sdf reconstruction by shadow ray supervision. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 175–185 (2023)

    Google Scholar 

  31. Liu, R., Wu, R., Hoorick, B.V., Tokmakov, P., Zakharov, S., Vondrick, C.: Zero-1-to-3: Zero-shot one image to 3d object. arXiv preprint arXiv:2309.16653 (2023)

  32. Liu, X., Bauer, S., Velten, A.: Phasor field diffraction based reconstruction for fast non-line-of-sight imaging systems. Nat. Commun. 11(1), 1645 (2020)

    Article  Google Scholar 

  33. Liu, X., et al.: Non-line-of-sight imaging using phasor-field virtual wave optics. Nature 572(7771), 620–623 (2019)

    Article  Google Scholar 

  34. Liu, X., Wang, J., Xiao, L., Fu, X., Qiu, L., Shi, Z.: Few-shot non-line-of-sight imaging with signal-surface collaborative regularization. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 13303–13312 (2022)

    Google Scholar 

  35. Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3d surface construction algorithm. In: SIGGRAPH, pp. 163–169. ACM (1987)

    Google Scholar 

  36. Luo, S., Hu, W.: Diffusion probabilistic models for 3d point cloud generation. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR) (2021)

    Google Scholar 

  37. Maeda, T., Wang, Y., Raskar, R., Kadambi, A.: Thermal non-line-of-sight imaging. In: Proc. IEEE Int. Conf. Computational Photography (ICCP), pp. 1–11. IEEE (2019)

    Google Scholar 

  38. Medin, S.C., Weiss, A., Durand, F., Freeman, W.T., Wornell, G.W.: Can shadows reveal biometric information? In: Proc. IEEE/CVF Winter Conf. on Applications of Computer Vision (WACV), pp. 869–879, January 2023

    Google Scholar 

  39. Metzler, C.A., et al.: Deep-inverse correlography: towards real-time high-resolution non-line-of-sight imaging. Optica 7(1), 63–71 (2020)

    Article  MathSciNet  Google Scholar 

  40. Murray-Bruce, J., Saunders, C., Goyal, V.K.: Occlusion-based computational periscopy with consumer cameras. In: Wavelets and Sparsity XVIII, vol. 11138, pp. 286–297. SPIE (2019)

    Google Scholar 

  41. Nichol, A., Jun, H., Dhariwal, P., Mishkin, P., Chen, M.: Point-e: a system for generating 3d point clouds from complex prompts (2022). https://arxiv.org/abs/2212.08751

  42. O’Toole, M., Lindell, D.B., Wetzstein, G.: Confocal non-line-of-sight imaging based on the light-cone transform. Nature 555(7696), 338–341 (2018)

    Article  Google Scholar 

  43. Pawlikowska, A.M., Halimi, A., Lamb, R.A., Buller, G.S.: Single-photon three-dimensional imaging at up to 10 kilometers range. Opt. Express 25(10), 11919–11931 (2017)

    Article  Google Scholar 

  44. Poole, B., Jain, A., Barron, J.T., Mildenhall, B.: Dreamfusion: text-to-3d using 2d diffusion. arXiv preprint arXiv:2309.16653 (2022)

  45. Popov, V., Vovk, I., Gogoryan, V., Sadekova, T., Kudinov, M.: Grad-tts: a diffusion probabilistic model for text-to-speech. In: ICML (2021)

    Google Scholar 

  46. Ramachandran, V.S.: Perception of shape from shading. Nature 331, 163–166 (1988)

    Article  Google Scholar 

  47. Rapp, J., et al.: Seeing around corners with edge-resolved transient imaging. Nat. Commun. 11(1), 5929 (2020)

    Article  Google Scholar 

  48. Rasul, K., Seward, C., Schuster, I., Vollgraf, R.: Autoregressive denoising diffusion models for multivariate probabilistic time series forecasting. In: Proc. Int. Conf. on Machine Learning (ICML) (2021)

    Google Scholar 

  49. Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 10684–10695, June 2022

    Google Scholar 

  50. Ronneberger, O., Fischer, P., Brox, T.: U-net: convolutional networks for biomedical image segmentation. In: Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp. 234–241. Lecture Notes in Computer Science. Springer (2015)

    Google Scholar 

  51. Saunders, C., Bose, R., Murray-Bruce, J., Goyal, V.K.: Multi-depth computational periscopy with an ordinary camera. In: Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), pp. 9299–9305 (2020)

    Google Scholar 

  52. Saunders, C., Murray-Bruce, J., Goyal, V.K.: Computational periscopy with an ordinary digital camera. Nature 565(7740), 472–475 (2019)

    Article  Google Scholar 

  53. Seidel, S., Rueda-Chacón, H., Cusini, I., Villa, F., Zappa, F., Yu, C., Goyal, V.K.: Non-line-of-sight snapshots and background mapping with an active corner camera. Nat. Commun. 14(1), 3677 (2023)

    Article  Google Scholar 

  54. Seidel, S.W., et al.: Corner occluder computational periscopy: estimating a hidden scene from a single photograph. In: Proc. IEEE Int. Conf. Computational Photography (ICCP), pp. 1–9. IEEE (2019)

    Google Scholar 

  55. Seidel, S.W., Murray-Bruce, J., Ma, Y., Yu, C., Freeman, W.T., Goyal, V.K.: Two-dimensional non-line-of-sight scene estimation from a single edge occluder. IEEE Trans. Comput. Imaging 7, 58–72 (2021)

    Article  MathSciNet  Google Scholar 

  56. Sharma, P., et al.: What you can learn by staring at a blank wall. In: Proc. IEEE/CVF Int. Conf. Computer Vision (ICCV), pp. 2330–2339, October 2021

    Google Scholar 

  57. Shim, J., Kang, C., Joo, K.: Diffusion-based signed distance fields for 3d shape generation. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 20887–20897, June 2023

    Google Scholar 

  58. Sohl-Dickstein, J., Weiss, E.A., Maheswaranathan, N., Ganguli, S.: Deep unsupervised learning using nonequilibrium thermodynamics. In: Proc. Int. Conf. on Machine Learning (ICML), pp. 2256–2265 (2015)

    Google Scholar 

  59. Somasundaram, S., Dave, A., Henley, C., Veeraraghavan, A., Raskar, R.: Role of transients in two-bounce non-line-of-sight imaging. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 9192–9201 (2023)

    Google Scholar 

  60. Song, Y., Ermon, S.: Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems 32 (2019)

    Google Scholar 

  61. Torralba, A., Freeman, W.T.: Accidental pinhole and pinspeck cameras: revealing the scene outside the picture. Int. J. Comput. Vis. 110(2), 92–112 (2014)

    Article  Google Scholar 

  62. Velten, A., Willwacher, T., Gupta, O., Veeraraghavan, A., Bawendi, M.G., Raskar, R.: Recovering three-dimensional shape around a corner using ultrafast time-of-flight imaging. Nat. Commun. 3(1), 745 (2012)

    Article  Google Scholar 

  63. Verlekar, T.T., Soares, L.D., Correia, P.L.: Gait recognition in the wild using shadow silhouettes. Image Vis. Comput. 76, 1–13 (2018)

    Article  Google Scholar 

  64. Wang, W., Yao, L., Chen, L., Lin, B., Cai, D., He, X., Liu, W.: Crossformer: a versatile vision transformer hinging on cross-scale attention. In: Proc. Int. Conf. on Learning Representations (ICLR) (2022)

    Google Scholar 

  65. Wang, Y., et al.: Accurate but fragile passive non-line-of-sight recognition. Commun. Phys. 4(1), 88 (2021)

    Article  Google Scholar 

  66. Yamashita, Y., Sakaue, F., Sato, J.: Recovering 3d shape and light source positions from non-planar shadows. In: Proc. IEEE/CVF Int. Conf. Pattern Recognition (ICPR), pp. 1775–1779 (2010)

    Google Scholar 

  67. Yang, B., et al.: Paint by example: Exemplar-based image editing with diffusion models. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 18381–18391 (2023)

    Google Scholar 

  68. Yang, G., Huang, Y., Hao, Z., Liu, M., Belongie, S., Hariharan, B.: Pointflow: 3d point cloud generation with continuous normalizing flows. In: Proc. IEEE/CVF Int. Conf. Computer Vision (ICCV) (2019)

    Google Scholar 

  69. Ye, J., Wang, P., Li, K., Shi, Y., Wang, H.: Consistent-1-to-3: consistent image to 3d view synthesis via geometry-aware diffusion models. arXiv preprint arXiv:2309.16653 (2024)

  70. Yedidia, A.B., Baradad, M., Thrampoulidis, C., Freeman, W.T., Wornell, G.W.: Using unknown occluders to recover hidden scenes. In: Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition (CVPR), pp. 12231–12239 (2019)

    Google Scholar 

  71. Zeng, X., et al.: Lion: latent point diffusion models for 3d shape generation. In: Advances in Neural Information Processing Systems (NeurIPS) (2022)

    Google Scholar 

  72. Zhou, L., Du, Y., Wu, J.: 3d shape generation and completion through point-voxel diffusion. In: Proc. IEEE/CVF Int. Conf. Computer Vision (ICCV), pp. 5806–5815 (2021)

    Google Scholar 

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Raji, F., Bruce, J.M. (2025). Soft Shadow Diffusion (SSD): Physics-Inspired Learning for 3D Computational Periscopy. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds) Computer Vision – ECCV 2024. ECCV 2024. Lecture Notes in Computer Science, vol 15138. Springer, Cham. https://doi.org/10.1007/978-3-031-72989-8_22

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