A. Agrawal, R. Chellappa, and R. Raskar, An algebraic approach to surface reconstruction from gradient fields, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1
DOI : 10.1109/ICCV.2005.31

A. Agrawal, R. Raskar, and R. Chellappa, What Is the Range of Surface Reconstructions from a Gradient Field?, Proceedings of the 9 th European Conference on Computer Vision (volume I), pp.578-591, 2006.
DOI : 10.1137/S1064827501389229

G. Aubert and J. F. Aujol, Poisson Skeleton Revisited: a New Mathematical Perspective, Journal of Mathematical Imaging and Vision, vol.66, issue.3, pp.149-159, 2014.
DOI : 10.1006/cviu.1997.0612

URL : https://hal.archives-ouvertes.fr/hal-00714250

H. Badri and H. Yahia, A Non-Local Low-Rank Approach to Enforce Integrability, IEEE Transactions on Image Processing, vol.25, issue.8, p.15, 2016.
DOI : 10.1109/TIP.2016.2570548

URL : https://hal.archives-ouvertes.fr/hal-01317151

H. Badri, H. Yahia, and D. Aboutajdine, Robust Surface Reconstruction via Triple Sparsity, 2014 IEEE Conference on Computer Vision and Pattern Recognition, p.16, 2014.
DOI : 10.1109/CVPR.2014.293

URL : https://hal.archives-ouvertes.fr/hal-00951627

M. Bähr and M. Breuß, An Improved Eikonal Equation for Surface Normal Integration, Proceedings of the 37 th German Conference on Pattern Recognition, p.13, 2015.

M. Bähr, M. Breuß, Y. Quéau, A. S. Boroujerdi, and J. D. Durou, Fast and accurate surface normal integration on non-rectangular domains, Computational Visual Media, vol.18, issue.2, pp.107-129, 2017.
DOI : 10.1023/A:1022104332058

J. Balzer, Shape from specular reflection in calibrated environments and the integration of spatial normal fields, 2011 18th IEEE International Conference on Image Processing, pp.21-24, 2011.
DOI : 10.1109/ICIP.2011.6116071

J. Balzer, A Gauss-Newton Method for the Integration of Spatial Normal Fields in Shape Space, Journal of Mathematical Imaging and Vision, vol.7, issue.4, pp.65-79, 2012.
DOI : 10.1137/080736612

J. Balzer and T. Mörwald, Isogeometric finite-elements methods and variational reconstruction tasks in vision — A perfect match, 2012 IEEE Conference on Computer Vision and Pattern Recognition, p.16, 2012.
DOI : 10.1109/CVPR.2012.6247855

J. Y. Chang, K. M. Lee, and S. U. Lee, Multiview normal field integration using level set methods, 2007 IEEE Conference on Computer Vision and Pattern Recognition, p.16, 2007.
DOI : 10.1109/CVPR.2007.383357

E. N. Coleman and R. Jain, Obtaining 3-dimensional shape of textured and specular surfaces using four-source photometry, Computer Graphics and Image Processing, vol.18, issue.4, pp.309-328, 1982.
DOI : 10.1016/0146-664X(82)90001-6

A. Crouzil, X. Descombes, and J. D. Durou, A multiresolution approach for shape shading coupling deterministic and stochastic optimization, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.11, pp.1416-1421, 2003.
DOI : 10.1109/TPAMI.2003.1240116

URL : https://hal.archives-ouvertes.fr/inria-00071578

Z. Du, A. Robles-kelly, and F. Lu, Robust Surface Reconstruction from Gradient Field Using the L1 Norm, 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications (DICTA 2007), pp.203-209
DOI : 10.1109/DICTA.2007.4426797

J. D. Durou, J. F. Aujol, and F. Courteille, Integrating the Normal Field of a Surface in the Presence of Discontinuities, Proceedings of the 7 th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, pp.261-273, 2009.
DOI : 10.1109/TPAMI.2007.70820

J. D. Durou and F. Courteille, Integration of a Normal Field without Boundary Condition, Proceedings of the 11 th IEEE International Conference on Computer Vision, 1 st Workshop on Photometric Analysis for Computer Vision
URL : https://hal.archives-ouvertes.fr/inria-00264852

S. Ettl, J. Kaminski, M. C. Knauer, and G. Häusler, Shape reconstruction from gradient data, Applied Optics, vol.47, issue.12, pp.2091-2097, 2008.
DOI : 10.1364/AO.47.002091

R. Fraile and E. R. Hancock, Combinatorial Surface Integration, 18th International Conference on Pattern Recognition (ICPR'06), pp.59-62
DOI : 10.1109/ICPR.2006.379

R. T. Frankot and R. Chellappa, A method for enforcing integrability in shape from shading algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.10, issue.4, pp.439-451, 1988.
DOI : 10.1109/34.3909

S. Galliani, M. Breuß, and Y. C. Ju, Fast and Robust Surface Normal Integration by a Discrete Eikonal Equation, Procedings of the British Machine Vision Conference 2012, p.16, 2012.
DOI : 10.5244/C.26.106

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, Shape and Spatially-Varying BRDFs From Photometric Stereo, Proceedings of the 10 th IEEE International Conference on Computer Vision (volume I), p.12, 2005.

P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol.24, p.5, 1985.
DOI : 10.1137/1.9781611972030

M. Harker and P. O-'leary, Least squares surface reconstruction from measured gradient fields, 2008 IEEE Conference on Computer Vision and Pattern Recognition, p.16, 2008.
DOI : 10.1109/CVPR.2008.4587414

M. Harker and P. O-'leary, Least squares surface reconstruction from gradients: Direct algebraic methods with spectral, Tikhonov, and constrained regularization, CVPR 2011, p.13, 2011.
DOI : 10.1109/CVPR.2011.5995427

M. Harker and P. O-'leary, Regularized Reconstruction of a Surface from its Measured Gradient Field, Journal of Mathematical Imaging and Vision, vol.19, issue.1, pp.46-70, 2015.
DOI : 10.1117/12.7972479

G. Healey and R. Jain, Depth Recovery from Surface Normals, Proceedings of the 7 th International Conference on Pattern Recognition, pp.894-896, 1984.

J. Ho, J. Lim, and M. H. Yang, Integrating Surface Normal Vectors Using Fast Marching Method, Proceedings of the 9 th European Conference on Computer Vision (volume III), pp.239-250, 2006.
DOI : 10.1007/11744078_19

B. K. Horn, Robot Vision, 1986.

B. K. Horn and M. J. Brooks, The variational approach to shape from shading, Computer Vision, Graphics, and Image Processing, vol.33, issue.2, pp.174-208, 1986.
DOI : 10.1016/0734-189X(86)90114-3

I. Horovitz and N. Kiryati, Bias Correction in Photometric Stereo Using Control Points, p.16, 2000.

I. Horovitz and N. Kiryati, Depth from gradient fields and control points: bias correction in photometric stereo, Image and Vision Computing, vol.22, issue.9, pp.681-694, 2004.
DOI : 10.1016/j.imavis.2004.01.005

S. Ikehata, D. Wipf, Y. Matsushita, and K. Aizawa, Photometric Stereo Using Sparse Bayesian Regression for General Diffuse Surfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.36, issue.9, pp.1816-1831, 2014.
DOI : 10.1109/TPAMI.2014.2299798

K. Ikeuchi, Constructing A Depth Map from Images, p.12, 1983.

B. Karaçali and W. Snyder, Reconstructing discontinuous surfaces from a given gradient field using partial integrability, Computer Vision and Image Understanding, vol.92, issue.1, pp.78-111, 2003.
DOI : 10.1016/S1077-3142(03)00095-X

B. Karaçali and W. Snyder, Noise Reduction in Surface Reconstruction from a Given Gradient Field, International Journal of Computer Vision, vol.60, issue.1, pp.25-44, 2004.
DOI : 10.1023/B:VISI.0000027788.50090.b6

R. Kimmel and I. Yavneh, An Algebraic Multigrid Approach for Image Analysis, SIAM Journal on Scientific Computing, vol.24, issue.4, pp.1218-1231, 2003.
DOI : 10.1137/S1064827501389229

R. Klette and K. Schlüns, Height Data from Gradient Fields, Proceedings of the Machine Vision Applications , Architectures, and Systems Integration, Proceedings of the International Society for Optical Engineering, pp.204-215, 1996.

P. Kovesi, Shapelets correlated with surface normals produce surfaces, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, pp.994-1001, 2005.
DOI : 10.1109/ICCV.2005.224

D. Lee, A Provably Convergent Algorithm for Shape from Shading, Proceedings of the DARPA Image Understanding Workshop, pp.489-496, 1985.

C. Miranda, Partial differential equations of elliptic type, second edn, 1970.

H. S. Ng, T. P. Wu, and C. K. Tang, Surface-from-Gradients with Incomplete Data for Single View Modeling, 2007 IEEE 11th International Conference on Computer Vision, p.16, 2007.
DOI : 10.1109/ICCV.2007.4409103

H. S. Ng, T. P. Wu, and C. K. Tang, Surface-from-Gradients without Discrete Integrability Enforcement: A Gaussian Kernel Approach, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.11, pp.2085-2099, 2010.

L. Noakes and R. Kozera, The 2-D Leap-Frog: Integrability, Noise, and Digitization, Digital and Image Geometry, pp.352-364
DOI : 10.1007/3-540-45576-0_21

L. Noakes and R. Kozera, Nonlinearities and Noise Reduction in 3-Source Photometric Stereo, Journal of Mathematical Imaging and Vision, vol.18, issue.2, pp.119-127, 2003.
DOI : 10.1023/A:1022104332058

L. Noakes, R. Kozera, and R. Klette, The Lawn-Mowing Algorithm for Noisy Gradient Vector Fields In: Vision Geometry VIII, Proceedings of the International Society for Optical Engineering, pp.305-316, 1999.

P. Pérez, M. Gangnet, and A. Blake, Poisson image editing, ACM Transactions on Graphics, vol.22, issue.3, pp.313-318, 2003.
DOI : 10.1145/882262.882269

N. Petrovic, I. Cohen, B. J. Frey, R. Koetter, and T. S. Huang, Enforcing integrability for surface reconstruction algorithms using belief propagation in graphical models, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, pp.743-748
DOI : 10.1109/CVPR.2001.990550

Y. Quéau, J. D. Durou, and J. F. Aujol, Variational Methods for Normal Integration (2017). (Preprint available at https://arxiv, pp.14-16

D. Reddy, A. Agrawal, and R. Chellappa, Enforcing Integrability by Error Correction using l1-minimization, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, p.16, 2009.

R. F. Saracchini, J. Stolfi, H. C. Leitão, G. A. Atkinson, and M. L. Smith, Multi-Scale Depth from Slope with Weights, Procedings of the British Machine Vision Conference 2010, p.16, 2010.
DOI : 10.5244/C.24.40

R. F. Saracchini, J. Stolfi, H. C. Leitão, G. A. Atkinson, and M. L. Smith, A robust multi-scale integration method to obtain the depth from gradient maps, Computer Vision and Image Understanding, vol.116, issue.8, pp.882-895, 2012.
DOI : 10.1016/j.cviu.2012.03.006

T. Simchony, R. Chellappa, and M. Shao, Direct analytical methods for solving Poisson equations in computer vision problems, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.5, pp.435-446, 1990.
DOI : 10.1109/34.55103

J. Stoer and R. Burlirsch, Introduction to Numerical Analysis, Text in Applied Mathematics, p.5, 2002.

A. Tankus and N. Kiryati, Photometric stereo under perspective projection, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, pp.611-616, 2005.
DOI : 10.1109/ICCV.2005.190

Y. Wang, J. Bu, N. Li, M. Song, and P. Tan, Detecting Discontinuities for Surface Reconstruction, Proceedings of the 21 st International Conference on Pattern Recognition, pp.2108-2111, 2012.

T. Wei and R. Klette, Depth Recovery from Noisy Gradient Vector Fields Using Regularization, Proceedings of the 10 th International Conference on Computer Analysis of Images and Patterns, pp.116-123, 2003.
DOI : 10.1007/978-3-540-45179-2_15

R. J. Woodham, Photometric Method For Determining Surface Orientation From Multiple Images, Optical Engineering, vol.19, issue.1, pp.139-144, 1980.
DOI : 10.1117/12.7972479

T. P. Wu and C. K. Tang, Visible Surface Reconstruction from Normals with Discontinuity Consideration, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (volume II), pp.1793-1800, 2006.

Z. Wu and L. Li, A line-integration based method for depth recovery from surface normals, Computer Vision, Graphics, and Image Processing, vol.43, issue.1, pp.53-66, 1988.
DOI : 10.1016/0734-189X(88)90042-4

W. Xie, Y. Zhang, C. C. Wang, and R. C. Chung, Surface-from-Gradients: An Approach Based on Discrete Geometry Processing, 2014 IEEE Conference on Computer Vision and Pattern Recognition, p.16, 2014.
DOI : 10.1109/CVPR.2014.282

Y. Yamaura, T. Nanya, H. Imoto, and T. Maekawa, Shape reconstruction from a normal map in terms of uniform bi-quadratic B-spline surfaces, Computer-Aided Design, vol.63, issue.14, pp.129-140, 2015.
DOI : 10.1016/j.cad.2015.01.005

A. L. Yuille and D. Snow, Shape and albedo from multiple images using integrability, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.158-164, 1997.
DOI : 10.1109/CVPR.1997.609314