M. Unger, T. Pock, M. Werlberger, and H. Bischof, A convex approach for variational super-resolution, Joint Pattern Recognition Symposium, pp.313-322, 2010.

J. Park, H. Kim, Y. Tai, M. S. Brown, and I. S. Kweon, High quality depth map upsampling for 3F-TOF cameras, Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp.1623-1630, 2011.

Y. Quéau, J. Durou, and J. Aujol, Normal Integration: A Survey, Journal of Mathematical Imaging and Vision, vol.60, issue.4, pp.576-593, 2018.

R. Basri and D. P. Jacobs, Lambertian reflectances and linear subspaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.2, pp.218-233, 2003.

R. Ramamoorthi and P. Hanrahan, An Efficient Representation for Irradiance Environment Maps, Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques, pp.497-500, 2001.

B. Goldlücke, M. Aubry, K. Kolev, and D. Cremers, A superresolution framework for high-accuracy multiview reconstruction, International Journal of Computer Vision, vol.106, issue.2, pp.172-191, 2014.

R. Maier, J. Stückler, and D. Cremers, Super-resolution keyframe fusion for 3D modeling with high-quality textures, Proceedings of the International Conference on 3D Vision (3DV), pp.536-544, 2015.

S. Schuon, C. Theobalt, J. Davis, and S. Thrun, Lidarboost: Depth superresolution for TOF 3D shape scanning, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp.343-350, 2009.

O. M. Aodha, N. D. Campbell, A. Nair, and G. J. Brostow, Patch based synthesis for single depth image super-resolution, Proceedings of the European Conference on Computer Vision (ECCV), pp.71-84, 2012.

J. Xie, R. S. Feris, and M. Sun, Edge-guided single depth image super resolution, IEEE Transactions on Image Processing, vol.25, issue.1, pp.428-438, 2016.

M. Hornácek, C. Rhemann, M. Gelautz, and C. Rother, Depth super resolution by rigid body self-similarity in 3D, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.1123-1130, 2013.

J. Li, Z. Lu, G. Zeng, R. Gan, and H. Zha, Similarity-aware patchwork assembly for depth image super-resolution, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.3374-3381, 2014.

J. Xie, R. S. Feris, S. Yu, and M. Sun, Joint super resolution and denoising from a single depth image, IEEE Transactions on Multimedia, vol.17, issue.9, pp.1525-1537, 2015.

D. Ferstl, M. Rüther, and H. Bischof, Variational depth superresolution using example-based edge representations, Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp.513-521, 2015.

G. Riegler, M. Rüther, and H. Bischof, ATGV-net: accurate depth super-resolution, Proceedings of the European Conference on Computer Vision (ECCV), pp.268-284, 2016.

B. K. Horn, Shape From Shading: A Method for Obtaining the Shape of a Smooth Opaque Object From One View, 1970.

M. Breuß, E. Cristiani, J. Durou, M. Falcone, and O. Vogel, Perspective shape from shading: Ambiguity analysis and numerical approximations, SIAM Journal on Imaging Sciences, vol.5, issue.1, pp.311-342, 2012.

J. Durou, M. Falcone, and M. Sagona, Numerical Methods for Shape-from-shading: A New Survey with Benchmarks, Computer Vision and Image Understanding, vol.109, pp.22-43, 2008.

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, Shape-fromshading: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.8, pp.690-706, 1999.

B. K. Horn and M. J. Brooks, Computer Vision, Graphics, and Image Processing, vol.33, pp.174-208, 1986.

K. Ikeuchi and B. K. Horn, Numerical shape from shading and occluding boundaries, Artificial intelligence, vol.17, issue.1-3, pp.141-184, 1981.

E. Cristiani and M. Falcone, Fast semi-lagrangian schemes for the eikonal equation and applications, SIAM Journal on Numerical Analysis, vol.45, issue.5, 1979.

M. Falcone and M. Sagona, An algorithm for the global solution of the shape-from-shading model, Proceedings of the International Conference on Image Analysis and Processing, pp.596-603, 1997.

P. Lions, E. Rouy, and A. Tourin, Shape-from-shading, viscosity solutions and edges, Numerische Mathematik, vol.64, issue.1, pp.323-353, 1993.

E. Rouy and A. Tourin, A viscosity solutions approach to shapefrom-shading, SIAM Journal on Numerical Analysis, vol.29, issue.3, pp.867-884, 1992.

E. H. Adelson and A. P. Pentland, Perception as Bayesian inference, The perception of shading and reflectance, pp.409-423, 1996.

R. Huang and W. A. Smith, Shape-from-shading under complex natural illumination, Proceedings of the IEEE International Conference on Image Processing, pp.13-16, 2011.

M. K. Johnson and E. H. Adelson, Shape estimation in natural illumination, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.2553-2560, 2011.

S. R. Richter and S. Roth, Discriminative shape from shading in uncalibrated illumination, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.1128-1136, 2015.

Y. Quéau, J. Mélou, F. Castan, D. Cremers, and J. Durou, A Variational Approach to Shape-from-shading Under Natural Illumination, Energy Minimization Methods for Computer Vision and Pattern Recognition, pp.342-357, 2017.

J. Barron and J. Malik, Shape, illumination, and reflectance from shading, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.37, issue.8, pp.1670-1687, 2015.

R. J. Woodham, Photometric Method for Determining Surface Orientation from Multiple Images, Optical Engineering, vol.19, issue.1, pp.139-144, 1980.

H. Hayakawa, Photometric stereo under a light source with arbitrary motion, Journal of the Optical Society of America A, vol.11, issue.11, pp.3079-3089, 1994.

P. N. Belhumeur, D. J. Kriegman, and A. L. Yuille, The bas-relief ambiguity, International Journal of Computer Vision, vol.35, issue.1, pp.33-44, 1999.

R. Basri, D. W. Jacobs, and I. Kemelmacher, Photometric stereo with general, unknown lighting, International Journal of Computer Vision, vol.72, issue.3, pp.239-257, 2007.

N. G. Alldrin, S. P. Mallick, and D. J. Kriegman, Resolving the generalized bas-relief ambiguity by entropy minimization, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2007.

T. Papadhimitri and P. Favaro, A closed-form, consistent and robust solution to uncalibrated photometric stereo via local diffuse reflectance maxima, International Journal of Computer Vision, vol.107, issue.2, pp.139-154, 2014.

Y. Quéau, F. Lauze, and J. Durou, Solving Uncalibrated Photometric Stereo using Total Variation, Journal of Mathematical Imaging and Vision, vol.52, issue.1, pp.87-107, 2015.

F. Lu, X. Chen, I. Sato, and Y. Sato, Symps: Brdf symmetry guided photometric stereo for shape and light source estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.40, issue.1, pp.221-234, 2018.

Z. Mo, B. Shi, F. Lu, S. Yeung, and Y. Matsushita, Uncalibrated photometric stereo under natural illumination, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.2936-2945, 2018.

B. Shi, Z. Mo, Z. Wu, D. Duan, S. K. Yeung et al., A benchmark dataset and evaluation for non-lambertian and uncalibrated photometric stereo, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.41, issue.2, pp.271-284, 2019.

Y. Quéau, T. Wu, F. Lauze, J. Durou, and D. Cremers, A Non-Convex Variational Approach to Photometric Stereo under Inaccurate Lighting, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR, pp.350-359, 2017.

S. Ikehata, CNN-PS: CNN-based photometric stereo for general non-convex surfaces, Proceedings of the European Conference on Computer Vision (ECCV), pp.3-18, 2018.

G. Chen, K. Han, B. Shi, Y. Matsushita, and K. K. Wong, Selfcalibrating deep photometric stereo networks, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.

G. Choe, J. Park, Y. Tai, and I. S. Kweon, Refining geometry from depth sensors using IR shading images, International Journal of Computer Vision, vol.122, issue.1, pp.1-16, 2017.

R. Maier, K. Kim, D. Cremers, J. Kautz, and M. Nießner, Intrinsic3d: High-quality 3D reconstruction by joint appearance and geometry optimization with spatially-varying lighting, Proceedings of the IEEE International Conference on Computer Vision (ICCV, pp.3114-3122, 2017.

M. Zollhöfer, A. Dai, M. Innman, C. Wu, M. Stamminger et al., Shading-based refinement on volumetric signed distance functions, ACM Transactions on Graphics, vol.34, issue.4, pp.1-96, 2015.

Y. Han, J. Lee, and I. S. Kweon, High Quality Shape from a Single RGB-D Image under Uncalibrated Natural Illumination, Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp.1617-1624, 2013.

K. Kim, A. Torii, and M. Okutomi, Joint estimation of depth, reflectance and illumination for depth refinement, Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp.199-207, 2015.

R. Or-el, R. Hershkovitz, A. Wetzler, G. Rosman, A. M. Bruckstein et al., Real-time depth refinement for specular objects, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.4378-4386, 2016.

R. Or-el, G. Rosman, A. Wetzler, R. Kimmel, and A. Bruckstein, RGBD-Fusion: Real-Time High Precision Depth Recovery, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.5407-5416, 2015.

C. Wu, M. Zollhöfer, M. Nießner, M. Stamminger, S. Izadi et al., Real-time shading-based refinement for consumer depth cameras, ACM Transactions on Graphics, vol.33, issue.6, pp.1-200, 2014.

L. Yu, S. Yeung, Y. Tai, and S. Lin, Shading-based shape refinement of RGB-D images, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.1415-1422, 2013.

R. Anderson, B. Stenger, and R. Cipolla, Augmenting depth camera output using photometric stereo, Proceedings of the IAPR Conference on Machine Vision Applications (MVA), pp.369-372, 2011.

A. Chatterjee and V. M. Govindu, Photometric refinement of depth maps for multi-albedo objects, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.933-941, 2015.

L. Xie, Y. Xu, X. Zhang, W. Bao, C. Tong et al., A selfcalibrated photo-geometric depth camera, The Visual Computer, 2018.

Y. Zhang, Q. Zhang, and W. Feng, High-Resolution Depth Refinement by Photometric and Multi-shading Constraints, PRICAI 2018: Trends in Artificial Intelligence, pp.201-209, 2018.

J. Diebel and S. Thrun, An application of Markov random fields to range sensing, Advances in Neural Information Processing Systems, pp.291-298, 2006.

D. Ferstl, C. Reinbacher, R. Ranftl, M. Rüther, and H. Bischof, Image guided depth upsampling using anisotropic total generalized variation, Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp.993-1000, 2013.

Q. Yang, R. Yang, J. Davis, and D. Nistér, Spatial-depth super resolution for range images, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2007.

B. Li, Y. Zhou, Y. Zhang, and A. Wang, Depth image superresolution based on joint sparse coding, Pattern Recognition Letters, 2019.

T. Hui, C. C. Loy, and X. Tang, Depth map super-resolution by deep multi-scale guidance, Proceedings of European Conference on Computer Vision (ECCV), pp.353-369, 2016.

P. Tan, S. Lin, and L. Quan, Subpixel photometric stereo, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.8, pp.1460-1471, 2008.

S. Chaudhuri and M. V. Joshi, Motion-free super-resolution, 2005.

Z. Lu, Y. Tai, F. Deng, M. Ben-ezra, and M. S. Brown, A 3D imaging framework based on high-resolution photometricstereo and low-resolution depth, International Journal of Computer Vision, vol.102, issue.1-3, pp.18-32, 2013.

B. Haefner, Y. Quéau, T. Möllenhoff, and D. Cremers, Fight ill-posedness with ill-posedness: Single-shot variational depth super-resolution from shading, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.164-174, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02118545

S. Peng, B. Haefner, Y. Quéau, and D. Cremers, Depth superresolution meets uncalibrated photometric stereo, Proceedings of the IEEE International Conference on Computer Vision (ICCV) Workshops, pp.2961-2968, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02118570

D. Mumford, Bayesian rationale for the variational formulation," in Geometry-driven diffusion in computer vision, pp.135-146, 1994.

G. Graber, J. Balzer, S. Soatto, and T. Pock, Efficient minimalsurface regularization of perspective depth maps in variational stereo, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.511-520, 2015.

E. H. Land, The retinex theory of color vision, Scientific American, vol.237, issue.6, pp.108-120, 1977.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers, Foundations and Trends in Machine Learning, vol.3, issue.1, pp.1-122, 2011.

J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, vol.55, issue.1, pp.293-318, 1992.

R. Glowinski and A. Marroco, Sur l'approximation, pa? eléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires, vol.9, pp.41-76, 1975.

E. Strekalovskiy and D. Cremers, Real-time minimization of the piecewise smooth Mumford-Shah functional, Proceedings of the European Conference on Computer Vision (ECCV), pp.127-141, 2014.

M. Schmidt, minFunc: unconstrained differentiable multivariate optimization in Matlab, 2005.

D. C. Liu and J. , On the limited memory BFGS method for large scale optimization, Mathematical programming, vol.45, issue.1, pp.503-528, 1989.

K. He, J. Sun, and X. Tang, Guided image filtering, IEEE Transactions on Pattern Analysis and Machine Intelligence, issue.6, pp.1397-1409, 2013.

J. Shen, X. Yang, Y. Jia, and X. Li, Intrinsic images using optimization, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.3481-3487, 2011.

Q. Fan, J. Yang, G. Hua, B. Chen, and D. Wipf, Revisiting deep intrinsic image decompositions, Proceedings of The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.8944-8952, 2018.

C. Li, K. Zhou, and S. Lin, Intrinsic face image decomposition with human face priors, Proceedings of the European Conference on Computer Vision (ECCV), pp.218-233, 2014.

D. Eigen, C. Puhrsch, and R. Fergus, Depth map prediction from a single image using a multi-scale deep network, Advances in Neural Information Processing Systems, pp.2366-2374, 2014.

G. Trigeorgis, P. Snape, I. Kokkinos, and S. Zafeiriou, Face normals "in-the-wild" using fully convolutional networks, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR, pp.38-47, 2017.

Z. Shu, E. Yumer, S. Hadap, K. Sunkavalli, E. Shechtman et al., Neural face editing with intrinsic image disentangling, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR, pp.5444-5453, 2017.

N. Wang, Y. Zhang, Z. Li, Y. Fu, W. Liu et al., Pixel2mesh: Generating 3d mesh models from single rgb images, Proceedings of the European Conference on Computer Vision (ECCV), 2018.

S. Sengupta, A. Kanazawa, C. D. Castillo, and D. W. Jacobs, SfSNet: Learning Shape, Refectance and Illuminance of Faces in the Wild, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.6296-6305, 2018.

J. Shi, Y. Dong, H. Su, and S. X. Yu, Learning non-lambertian object intrinsics across shapenet categories, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR, pp.5844-5853, 2017.

W. Ma, T. Hawkins, P. Peers, C. Chabert, M. Weiss et al., Rapid acquisition of specular and diffuse normal maps from polarized spherical gradient illumination, Proceedings of the 18th Eurographics Conference on Rendering Techniques, pp.183-194, 2007.

G. Stratou, A. Ghosh, P. Debevec, and L. Morency, Effect of illumination on automatic expression recognition: A novel 3d relightable facial database, Face and Gesture, pp.611-618, 2011.

O. Ronneberger, P. Fischer, and T. Brox, U-net: Convolutional networks for biomedical image segmentation, Medical Image Computing and Computer-Assisted Intervention (MICCAI), pp.234-241, 2015.

M. Werlberger, W. Trobin, T. Pock, A. Wedel, D. Cremers et al., Anisotropic Huber-L1 Optical Flow, Proceedings of the British Machine Vision Conference, vol.11, pp.108-109, 2009.

L. Chen, Y. Zheng, B. Shi, A. Subpa-asa, and I. Sato, A microfacet-based reflectance model for photometric stereo with highly specular surfaces, Proceedings of the IEEE International Conference on Computer Vision (ICCV, pp.3162-3170, 2017.

M. Gardner, K. Sunkavalli, E. Yumer, X. Shen, E. Gambaretto et al., Learning to predict indoor illumination from a single image, ACM Transactions on Graphics, vol.36, issue.6, pp.1-176, 2017.

Y. Quéau, B. Durix, T. Wu, D. Cremers, F. Lauze et al., LED-based Photometric Stereo: Modeling, Calibration and Numerical Solution, Journal of Mathematical Imaging and Vision, vol.60, issue.3, pp.313-340, 2018.

D. Frolova, D. Simakov, and R. Basri, Accuracy of spherical harmonic approximations for images of Lambertian objects under far and near lighting, Proceedings of the European Conference on Computer Vision (ECCV), pp.574-587, 2004.

M. M. Takuya-narihira and S. X. Yu, Direct intrinsics: Learning albedo-shading decomposition by convolutional regression, Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2015.

D. J. Butler, J. Wulff, G. B. Stanley, and M. J. Black, A naturalistic open source movie for optical flow evaluation, Proceedings of the European Conference on Computer Vision (ECCV), pp.611-625, 2012.

R. Grosse, M. K. Johnson, E. H. Adelson, and W. T. Freeman, Ground truth dataset and baseline evaluations for intrinsic image algorithms, Proceedings of the IEEE International Conference on Computer Vision, pp.2335-2342, 2009.

A. X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang et al., ShapeNet: An Information-Rich 3D Model Repository, 2015.

M. Levoy, J. Gerth, B. Curless, and K. Pull, The stanford 3d scanning repository, 2005.

, The joyful yell, p.897412, 2015.

K. Khoshelham and S. O. Elberink, Accuracy and resolution of Kinect depth data for indoor mapping applications, Sensors, vol.12, issue.2, pp.1437-1454, 2012.

Z. Wang and A. C. Bovik, Mean squared error: Love it or leave it? a new look at signal fidelity measures, IEEE signal processing magazine, vol.26, issue.1, pp.98-117, 2009.

R. Maier, K. Kim, D. Cremers, J. Kautz, and M. Nießner, Intrinsic3D Dataset, 2017.

Y. Quéau, J. Durou, and J. Aujol, Variational methods for normal integration, Journal of Mathematical Imaging and Vision, vol.60, issue.4, pp.609-632, 2018.