{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T11:10:06Z","timestamp":1748776206631,"version":"3.41.0"},"reference-count":86,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,2,10]],"date-time":"2016-02-10T00:00:00Z","timestamp":1455062400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1007\/s10851-016-0636-x","type":"journal-article","created":{"date-parts":[[2016,2,10]],"date-time":"2016-02-10T22:40:08Z","timestamp":1455144008000},"page":"153-178","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Analysis and Approximation of Some Shape-from-Shading Models for Non-Lambertian Surfaces"],"prefix":"10.1007","volume":"55","author":[{"given":"Silvia","family":"Tozza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maurizio","family":"Falcone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,2,10]]},"reference":[{"key":"636_CR1","doi-asserted-by":"crossref","unstructured":"Ahmed, A., Farag, A.: A new formulation for shape from shading for non-Lambertian surfaces. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1817\u20131824 (2006)","DOI":"10.1109\/CVPR.2006.35"},{"key":"636_CR2","doi-asserted-by":"crossref","unstructured":"Ahmed, A.H., Farag, A.A.: Shape from Shading under various imaging conditions. In: IEEE International Conference on Computer Vision and Pattern Recognition CVPR\u201907, pp. X1\u2013X8. Minneapolis (2007)","DOI":"10.1109\/CVPR.2007.383286"},{"key":"636_CR3","doi-asserted-by":"crossref","unstructured":"Bakshi, S., Yang, Y.H.: Shape-from-Shading for non-Lambertian surfaces. In: Proceedings of IEEE International Conference on Image Processing (ICIP), pp. 130\u2013134 (1994)","DOI":"10.1109\/ICIP.1994.413545"},{"key":"636_CR4","volume-title":"Solutions de viscosit\u00e9 des \u00e9quations de Hamilton-Jacobi","author":"G Barles","year":"1994","unstructured":"Barles, G.: Solutions de viscosit\u00e9 des \u00e9quations de Hamilton-Jacobi. Springer, Berlin (1994)"},{"issue":"5","key":"636_CR5","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1109\/TPAMI.2008.135","volume":"31","author":"S Biswas","year":"2009","unstructured":"Biswas, S., Aggarwal, G., Chellappa, R.: Robust estimation of albedo for illumination-invariant matching and shape recovery. IEEE Trans. Pattern Anal. Mach. Intell. 31(5), 884\u2013899 (2009)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"2","key":"636_CR6","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF00128131","volume":"7","author":"M Brooks","year":"1992","unstructured":"Brooks, M., Chojnacki, W., Kozera, R.: Impossible and ambiguous shading patterns. Int. J. Comput. Vis. 7(2), 119\u2013126 (1992)","journal-title":"Int. J. Comput. Vis."},{"key":"636_CR7","unstructured":"Brooks, M., Horn, B.: Shape and source from shading. In: Proceedings of the Ninth International Joint Conference on Artificial Intelligence (vol. II), pp. 932\u2013936. Los Angeles (1985)"},{"key":"636_CR8","unstructured":"Bruss, A.: The image irradiance equation: Its solution and application. Technical report ai-tr-623, Massachusetts Institute of Technology (1981)"},{"key":"636_CR9","doi-asserted-by":"crossref","unstructured":"Camilli, F., Falcone, M.: An approximation scheme for the maximal solution of the shape from shading model. In: Proceedings of the IEEE International Conference on Image Processing (vol. I), vol.\u00a01, pp. 49\u201352. Lausanne (1996). doi: 10.1109\/ICIP.1996.559430","DOI":"10.1109\/ICIP.1996.559430"},{"issue":"5","key":"636_CR10","doi-asserted-by":"crossref","first-page":"1540","DOI":"10.1137\/S003614299834798X","volume":"38","author":"F Camilli","year":"2000","unstructured":"Camilli, F., Gr\u00fcne, L.: Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. SIAM J. Numer. Anal. 38(5), 1540\u20131560 (2000)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"636_CR11","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1512\/iumj.1999.48.1678","volume":"48","author":"F Camilli","year":"1999","unstructured":"Camilli, F., Siconolfi, A.: Maximal subsolutions of a class of degenerate Hamilton-Jacobi problems. Indiana Univ. Math. J. 48(3), 1111\u20131131 (1999)","journal-title":"Indiana Univ. Math. J."},{"key":"636_CR12","doi-asserted-by":"crossref","unstructured":"Carlini, E., Falcone, M., Festa, A.: A brief survey on semi-lagrangian schemes for image processing. In: M. Breuss, A. Bruckstein, P. Maragos (eds.) Innovations for Shape Analysis: Models and Algorithms, pp. 191\u2013218. Springer (2013). ISBN: 978-3-642-34140-3","DOI":"10.1007\/978-3-642-34141-0_9"},{"issue":"1","key":"636_CR13","first-page":"1","volume":"11","author":"A Chambolle","year":"1994","unstructured":"Chambolle, A.: A uniqueness result in the theory of stereo vision: coupling shape from shading and binocular information allows unambiguous depth reconstruction. Ann. l\u2019Ist. Henri Poincar\u00e8 11(1), 1\u201316 (1994)","journal-title":"Ann. l\u2019Ist. Henri Poincar\u00e8"},{"key":"636_CR14","doi-asserted-by":"crossref","unstructured":"Courteille, F., Crouzil, A., Durou, J.D., Gurdjos, P.: Towards shape from Shading under realistic photographic conditions. In: Proceedings of the 17th International Conference on Pattern Recognition, vol. 2, pp. 277\u2013280. Cambridge (2004)","DOI":"10.1109\/ICPR.2004.1334160"},{"issue":"5","key":"636_CR15","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s00138-006-0062-y","volume":"18","author":"F Courteille","year":"2007","unstructured":"Courteille, F., Crouzil, A., Durou, J.D., Gurdjos, P.: Shape from shading for the digitization of curved documents. Mach. Vis. Appl. 18(5), 301\u2013316 (2007)","journal-title":"Mach. Vis. Appl."},{"key":"636_CR16","unstructured":"Daniel, P., Durou, J.D.: From deterministic to stochastic methods for shape from shading. In: Proceedings of the Fourth Asian Conference on Computer Vision, pp. 187\u2013192. Taipei, Taiwan (2000)"},{"issue":"423","key":"636_CR17","first-page":"283","volume":"11","author":"JV Diggelen","year":"1951","unstructured":"Diggelen, J.V.: A photometric investigation of the slopes and heights of the ranges of hills in the maria of the moon. Bull. Astron. Inst. Neth. 11(423), 283\u2013290 (1951)","journal-title":"Bull. Astron. Inst. Neth."},{"key":"636_CR18","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/978-3-642-03641-5_20","volume":"5681","author":"JD Durou","year":"2009","unstructured":"Durou, J.D., Aujol, J.F., Courteille, F.: Integrating the normal field of a surface in the presence of discontinuities. Energy Minim. Methods Comput. Vis. Pattern Recogn. (EMMCVPR) 5681, 261\u2013273 (2009)","journal-title":"Energy Minim. Methods Comput. Vis. Pattern Recogn. (EMMCVPR)"},{"issue":"1","key":"636_CR19","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.cviu.2007.09.003","volume":"109","author":"JD Durou","year":"2008","unstructured":"Durou, J.D., Falcone, M., Sagona, M.: Numerical methods for shape from shading: a new survey with benchmarks. Comput. Vis. Image Underst. 109(1), 22\u201343 (2008)","journal-title":"Comput. Vis. Image Underst."},{"key":"636_CR20","unstructured":"Falcone, M.: Numerical solution of dynamic programming equations. In Bardi, M., Dolcetta, I.C., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, pp. 471\u2013504 (1997)"},{"key":"636_CR21","doi-asserted-by":"crossref","unstructured":"Falcone, M., Ferretti, R.: Semi-Lagrangian approximation schemes for linear and hamilton-jacobi equations. SIAM (2014)","DOI":"10.1137\/1.9781611973051"},{"key":"636_CR22","doi-asserted-by":"crossref","unstructured":"Falcone, M., Sagona, M.: An algorithm for the global solution of the shape from shading model. In: Proceedings of the Ninth International Conference on Image Analysis and Processing (vol. I), vol. 1310 of Lecture Notes in Computer Science, pp. 596\u2013603. Florence (1997)","DOI":"10.1007\/3-540-63507-6_250"},{"key":"636_CR23","doi-asserted-by":"crossref","unstructured":"Falcone, M., Sagona, M., Seghini, A.: A scheme for the shape\u2013from\u2013shading model with \u201cblack shadows\u201d. Numer. Math. Adv. Appl. 503\u2013512 (2003)","DOI":"10.1007\/978-88-470-2089-4_47"},{"key":"636_CR24","unstructured":"Fassold, H., Danzl, R., Schindler, K., Bischof, H.: Reconstruction of archaeological finds using shape from stereo and shape from shading. In: Proceedings of the 9th Computer Vision Winter Workshop. Piran, pp. 21\u201330 (2004)"},{"key":"636_CR25","doi-asserted-by":"crossref","unstructured":"Favaro, P., Papadhimitri, T.: A closed-form solution to uncalibrated photometric stereo via diffuse maxima. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 821\u2013828 (2012)","DOI":"10.1109\/CVPR.2012.6247754"},{"issue":"4","key":"636_CR26","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/34.3909","volume":"10","author":"R Frankot","year":"1988","unstructured":"Frankot, R., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439\u2013451 (1988)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"12","key":"636_CR27","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1016\/j.asr.2013.09.036","volume":"53","author":"A Grumpe","year":"2014","unstructured":"Grumpe, A., Belkhir, F., W\u00f6hler, C.: Construction of lunar DEMs based on reflectance modelling. Adv. Sp. Res. 53(12), 1735\u20131767 (2014)","journal-title":"Adv. Sp. Res."},{"key":"636_CR28","unstructured":"Horn, B.: Shape from shading: a method for obtaining the shape of a smooth opaque object from one view. Ph.D. Thesis, Massachusetts Institute of Technology (1970)"},{"key":"636_CR29","first-page":"115","volume-title":"The Psychology of Computer Vision","author":"B Horn","year":"1975","unstructured":"Horn, B.: Obtaining shape from shading information. In: Winston, P.H. (ed.) The Psychology of Computer Vision, vol. 4, pp. 115\u2013155. McGraw-Hill, New York (1975)"},{"issue":"2","key":"636_CR30","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/0734-189X(86)90114-3","volume":"33","author":"B Horn","year":"1986","unstructured":"Horn, B., Brooks, M.: The variational approach to shape from shading. Comput. Vis. Graph. Image Process. 33(2), 174\u2013208 (1986)","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"636_CR31","volume-title":"Shape from Shading (Artificial Intelligence)","author":"B Horn","year":"1989","unstructured":"Horn, B., Brooks, M.: Shape from Shading (Artificial Intelligence). The MIT Press, Cambridge (1989)"},{"issue":"1\u20133","key":"636_CR32","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0004-3702(81)90023-0","volume":"17","author":"K Ikeuchi","year":"1981","unstructured":"Ikeuchi, K., Horn, B.K.: Numerical shape from shading and occluding boundaries. Artif. Intell. 17(1\u20133), 141\u2013184 (1981)","journal-title":"Artif. Intell."},{"key":"636_CR33","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1080\/03605309508821168","volume":"20","author":"H Ishii","year":"1995","unstructured":"Ishii, H., Ramaswamy, M.: Uniqueness results for a class of Hamilton\u2013Jacobi equations with singular coefficients. Commun. Partial Differ. Equ. 20, 2187\u20132213 (1995)","journal-title":"Commun. Partial Differ. Equ."},{"key":"636_CR34","doi-asserted-by":"crossref","unstructured":"Ju, Y., Breu\u00df, M., Bruhn, A., Galliani, S.: Shape from shading for rough surfaces: analysis of the Oren-Nayar model. In: Proceedings of the British Machine Vision Conference (BMVC), pp. 104.1\u2013104.11. BMVA Press (2012). doi: 10.5244\/C.26.104","DOI":"10.5244\/C.26.104"},{"key":"636_CR35","doi-asserted-by":"crossref","unstructured":"Ju, Y., Tozza, S., Breu\u00df, M., Bruhn, A., Kleefeld, A.: Generalised perspective shape from shading with Oren-Nayar reflectance. In: Proceedings of the 24th British Machine Vision Conference (BMVC 2013), pp. 42.1\u201342.11. BMVA Press, Bristol (2013)","DOI":"10.5244\/C.27.42"},{"issue":"3","key":"636_CR36","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1023\/A:1012235914303","volume":"44","author":"J Kain","year":"2001","unstructured":"Kain, J., Ostrov, D.: Numerical shape from shading for discontinuous photographic images. Int. J. Comput. Vis. 44(3), 163\u2013173 (2001)","journal-title":"Int. J. Comput. Vis."},{"issue":"1","key":"636_CR37","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0096-3003(91)90001-4","volume":"44","author":"R Kozera","year":"1991","unstructured":"Kozera, R.: Existence and uniqueness in photometric stereo. Appl. Math. Comput. 44(1), 103 (1991)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"636_CR38","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1023\/A:1008249420974","volume":"7","author":"R Kozera","year":"1997","unstructured":"Kozera, R.: Uniqueness in shape from shading revisited. J. Math. Imaging Vis. 7(2), 123\u2013138 (1997)","journal-title":"J. Math. Imaging Vis."},{"key":"636_CR39","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1070\/SM1975v027n03ABEH002522","volume":"27","author":"SN Kruzkov","year":"1975","unstructured":"Kruzkov, S.N.: The generalized solution of the hamilton-jacobi equations of eikonal type i. Math. USSR Sbornik 27, 406\u2013446 (1975)","journal-title":"Math. USSR Sbornik"},{"issue":"3","key":"636_CR40","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/BF01388692","volume":"64","author":"P Lions","year":"1993","unstructured":"Lions, P., Rouy, E., Tourin, A.: Shape-from-shading, viscosity solutions and edges. Numer. Math. 64(3), 323\u2013353 (1993)","journal-title":"Numer. Math."},{"issue":"7","key":"636_CR41","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.pss.2006.03.002","volume":"54","author":"V Lohse","year":"2006","unstructured":"Lohse, V., Heipke, C., Kirk, R.L.: Derivation of planetary topography using multi-image shape-from-shading. Planetary Sp. Sci. 54(7), 661\u2013674 (2006)","journal-title":"Planetary Sp. Sci."},{"issue":"1","key":"636_CR42","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1137\/110857258","volume":"6","author":"R Mecca","year":"2013","unstructured":"Mecca, R., Falcone, M.: Uniqueness and approximation of a photometric shape-from-shading model. SIAM J. Imaging Sci. 6(1), 616\u2013659 (2013)","journal-title":"SIAM J. Imaging Sci."},{"key":"636_CR43","doi-asserted-by":"crossref","unstructured":"Mecca, R., Tozza, S.: Shape reconstruction of symmetric surfaces using photometric stereo. In: M. Breuss, A. Bruckstein, P. Maragos (eds.) Innovations for Shape Analysis: Models and Algorithms, pp. 219\u2013243. Springer (2013). ISBN: 978-3-642-34140-3","DOI":"10.1007\/978-3-642-34141-0_10"},{"issue":"2","key":"636_CR44","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1006\/cviu.1997.0613","volume":"66","author":"T Okatani","year":"1997","unstructured":"Okatani, T., Deguchi, K.: Shape reconstruction from an endoscope image by shape from shading technique for a point light source at the projection center. Comput. Vis. Image Underst. 66(2), 119\u2013131 (1997)","journal-title":"Comput. Vis. Image Underst."},{"issue":"2","key":"636_CR45","first-page":"163","volume":"54","author":"J Oliensis","year":"1991","unstructured":"Oliensis, J.: Shape from shading as a partially well-constrained problem. Comput. Vis. Graph. Image Process. 54(2), 163\u2013183 (1991)","journal-title":"Comput. Vis. Graph. Image Process."},{"issue":"2","key":"636_CR46","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF00128151","volume":"6","author":"J Oliensis","year":"1991","unstructured":"Oliensis, J.: Uniqueness in shape from shading. Int. J. Comput. Vis. 6(2), 75\u2013104 (1991)","journal-title":"Int. J. Comput. Vis."},{"key":"636_CR47","doi-asserted-by":"crossref","unstructured":"Oren, M., Nayar, S.: Diffuse reflectance from rough surfaces. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 763\u2013764 (1993)","DOI":"10.1109\/CVPR.1993.341163"},{"key":"636_CR48","doi-asserted-by":"crossref","unstructured":"Oren, M., Nayar, S.: Generalization of Lambert\u2019s reflectance model. In: Proceedings of the International Conference and Exhibition on Computer Graphics and Interactive Techniques (SIGGRAPH), pp. 239\u2013246 (1994)","DOI":"10.1145\/192161.192213"},{"key":"636_CR49","doi-asserted-by":"crossref","unstructured":"Oren, M., Nayar, S.: Seeing beyond Lambert\u2019s law. In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 269\u2013280 (1994)","DOI":"10.1007\/BFb0028360"},{"issue":"3","key":"636_CR50","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF01679684","volume":"14","author":"M Oren","year":"1995","unstructured":"Oren, M., Nayar, S.: Generalization of the Lambertian model and implications for machine vision. Int. J. Comput. Vis. 14(3), 227\u2013251 (1995)","journal-title":"Int. J. Comput. Vis."},{"issue":"6","key":"636_CR51","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1145\/360825.360839","volume":"18","author":"BT Phong","year":"1975","unstructured":"Phong, B.T.: Illumination for computer generated pictures. Commun. ACM 18(6), 311\u2013317 (1975)","journal-title":"Commun. ACM"},{"issue":"2","key":"636_CR52","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1051\/m2an:2006018","volume":"40","author":"E Prados","year":"2006","unstructured":"Prados, E., Camilli, F., Faugeras, O.: A viscosity solution method for shape-from-shading without image boundary data. ESAIM Math. Model. Numer. Anal. 40(2), 393\u2013412 (2006)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"636_CR53","unstructured":"Prados, E., Faugeras, O.: A mathematical and algorithmic study of the lambertian sfs problem for orthographic and pinhole cameras. Rapport de recherche 5005, Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis (2003)"},{"key":"636_CR54","doi-asserted-by":"crossref","unstructured":"Prados, E., Faugeras, O.: Perspective shape from shading and viscosity solutions. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 826\u2013831 (2003)","DOI":"10.1109\/ICCV.2003.1238433"},{"key":"636_CR55","doi-asserted-by":"crossref","unstructured":"Prados, E., Faugeras, O.: Shape from shading: a well-posed problem? In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. 870\u2013877 (2005)","DOI":"10.1109\/CVPR.2005.319"},{"key":"636_CR56","doi-asserted-by":"crossref","unstructured":"Prados, E., Faugeras, O., Rouy, E.: Shape from shading andviscosity solutions. In: A.\u00a0Heyden, G.\u00a0Sparr, M.\u00a0Nielsen,P.\u00a0Johansen (eds.) Computer Vision, ECCV 2002, Lecture Notes in Computer Science, vol. 2351, pp. 790\u2013804. Springer, Berlin\/Heidelberg (2002)","DOI":"10.1007\/3-540-47967-8_53"},{"issue":"1","key":"636_CR57","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10851-014-0512-5","volume":"52","author":"Y Qu\u00e9au","year":"2015","unstructured":"Qu\u00e9au, Y., Lauze, F., Durou, J.: Solving uncalibrated photometric stereo using total variation. J. Math. Imaging Vis. 52(1), 87\u2013107 (2015)","journal-title":"J. Math. Imaging Vis."},{"key":"636_CR58","doi-asserted-by":"crossref","unstructured":"Ragheb, H., Hancock, E.: Surface normals and height from non-lambertian image data. In: Proceedings of the International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), pp. 18\u201325 (2004)","DOI":"10.1109\/TDPVT.2004.1335136"},{"issue":"10","key":"636_CR59","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1016\/j.patcog.2005.03.025","volume":"38","author":"H Ragheb","year":"2005","unstructured":"Ragheb, H., Hancock, E.: Surface radiance correction for shape from shading. Pattern Recogn. 38(10), 1574\u20131595 (2005)","journal-title":"Pattern Recogn."},{"issue":"2","key":"636_CR60","first-page":"262","volume":"32","author":"T Rindfleisch","year":"1966","unstructured":"Rindfleisch, T.: Photometric method for lunar topography. Photogramm. Eng. 32(2), 262\u2013277 (1966)","journal-title":"Photogramm. Eng."},{"issue":"3","key":"636_CR61","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1137\/0729053","volume":"29","author":"E Rouy","year":"1992","unstructured":"Rouy, E., Tourin, A.: A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29(3), 867\u2013884 (1992)","journal-title":"SIAM J. Numer. Anal."},{"key":"636_CR62","unstructured":"Sagona, M.: Numerical methods for degenerate eikonal type equations and applications. Ph.D. thesis, Dipartimento di Matematica dell\u2018Universit\u00e0 di Napoli Federico II, Napoli (2001)"},{"issue":"2","key":"636_CR63","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1109\/TPAMI.2003.1177155","volume":"25","author":"D Samaras","year":"2003","unstructured":"Samaras, D., Metaxas, D.: Incorporating illumination constraints in deformable models for shape from shading and light direction estimation. IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 247\u2013264 (2003)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"636_CR64","doi-asserted-by":"crossref","unstructured":"Smith, W., Hancock, E.: Recovering facial shape and albedo using a statistical model of surface normal direction. In: 10th IEEE International Conference on Computer Vision (ICCV 2005), 2005, Beijing, pp. 588\u2013595 (2005)","DOI":"10.1109\/ICCV.2005.203"},{"issue":"6","key":"636_CR65","first-page":"955","volume":"20","author":"W Smith","year":"2006","unstructured":"Smith, W., Hancock, E.: Estimating facial albedo from a single image. IJPRAI 20(6), 955\u2013970 (2006)","journal-title":"IJPRAI"},{"issue":"4","key":"636_CR66","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1109\/TVCG.2010.62","volume":"17","author":"W Steffen","year":"2011","unstructured":"Steffen, W., Koning, N., Wenger, S., Morisset, C., Magnor, M.: Shape: a 3d modeling tool for astrophysics. IEEE Trans. Visual. Comput. Graph. 17(4), 454\u2013465 (2011)","journal-title":"IEEE Trans. Visual. Comput. Graph."},{"key":"636_CR67","unstructured":"Strat, T.: A numerical method for shape from shading from a single image. Master\u2019s thesis, Department of Electrical Engineering and Computer Science, Massachussetts Institute of Technology, Cambridge (1979)"},{"issue":"2","key":"636_CR68","first-page":"129","volume":"53","author":"R Szeliski","year":"1991","unstructured":"Szeliski, R.: Fast shape from shading. Comput. Vis. Graph. Image Process. 53(2), 129\u2013153 (1991)","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"636_CR69","doi-asserted-by":"crossref","unstructured":"Tankus, A., Kiryati, N.: Photometric stereo under perspective projection. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV), vol. 1, pp. 611\u2013616 (2005)","DOI":"10.1109\/ICCV.2005.190"},{"issue":"1","key":"636_CR70","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11263-005-4945-6","volume":"63","author":"A Tankus","year":"2005","unstructured":"Tankus, A., Sochen, N., Yeshurun, Y.: Shape-from-shading under perspective projection. Int. J. Comput. Vis. 63(1), 21\u201343 (2005)","journal-title":"Int. J. Comput. Vis."},{"key":"636_CR71","unstructured":"Tozza, S.: Analysis and approximation of non-Lambertian shape-from-shading models. Ph.D. thesis, Dipartimento di Matematica, Sapienza - Universit\u00e1 di Roma, Rome (2015)"},{"key":"636_CR72","doi-asserted-by":"crossref","unstructured":"Tozza, S., Falcone, M.: A semi-Lagrangian approximation of the Oren-Nayar PDE for the orthographic shape-from-shading problem. In: S. Battiato, J. Braz (eds.) Proceedings of the 9th International Conference on Computer Vision Theory and Applications (VISAPP), vol. 3, pp. 711\u2013716. SciTePress (2014)","DOI":"10.5220\/0004855007110716"},{"key":"636_CR73","doi-asserted-by":"crossref","unstructured":"Tozza, S., Falcone, M.: A comparison of non-lambertian models for the shape-from-shading problem. In: M. Breuss, A. Bruckstein, P. Maragos, S. Wuhrer (eds.) New Perspectives in Shape Analysis. Springer (2015)","DOI":"10.1007\/978-3-319-24726-7_2"},{"key":"636_CR74","doi-asserted-by":"crossref","unstructured":"Tozza, S., Mecca, R., Duocastella, M., Bue, A.D.: Direct differential photometric-stereo shape recovery of diffuse and specular surfaces. J. Math. Imaging Vis. (JMIV) (2016). doi: 10.1007\/s10851-016-0633-0","DOI":"10.1007\/s10851-016-0633-0"},{"key":"636_CR75","doi-asserted-by":"crossref","unstructured":"Vogel, O., Breu\u00df, M., Leichtweis, T., Weickert, J.: Fast shape from shading for phong-type surfaces. In: X.C. Tai, K.\u00a0M\u00f8rken, M.\u00a0Lysaker, K.A. Lie (eds.) Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, vol. 5567, pp. 733\u2013744. Springer (2009)","DOI":"10.1007\/978-3-642-02256-2_61"},{"key":"636_CR76","doi-asserted-by":"crossref","unstructured":"Vogel, O., Breu\u00df, M., Weickert, J.: Perspective shape from shading with non-Lambertian reflectance. In: Proceedings of the DAGM Symposium on Pattern Recognition, pp. 517\u2013526 (2008)","DOI":"10.1007\/978-3-540-69321-5_52"},{"key":"636_CR77","doi-asserted-by":"crossref","unstructured":"Vogel, O., Valgaerts, L., Breu\u00df, M., Weickert, J.: Making shape from shading work for real-world images. In: J.\u00a0Denzler, G.\u00a0Notni,H.\u00a0S\u00fc\u00dfe (eds.) Pattern Recognition, Lecture Notes in Computer Science, vol. 5748, pp. 191\u2013200. Springer, Berlin\/Heidelberg (2009)","DOI":"10.1007\/978-3-642-03798-6_20"},{"key":"636_CR78","unstructured":"Wikipedia: Mask of Agamemnon. http:\/\/en.wikipedia.org\/wiki\/Mask_of_Agamemnon"},{"issue":"11","key":"636_CR79","doi-asserted-by":"crossref","first-page":"2956","DOI":"10.1364\/JOSAA.11.002956","volume":"11","author":"L Wolff","year":"1994","unstructured":"Wolff, L.: Diffuse-reflectance model for smooth dielectric surfaces. J. Opt. Soc. Am. A 11(11), 2956\u20132968 (1994)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"1","key":"636_CR80","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1023\/A:1008017513536","volume":"30","author":"LB Wolff","year":"1998","unstructured":"Wolff, L.B., Nayar, S.K., Oren, M.: Improved diffuse reflection models for computer vision. Int. J. Comput. Vis. 30(1), 55\u201371 (1998)","journal-title":"Int. J. Comput. Vis."},{"issue":"1","key":"636_CR81","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1117\/12.7972479","volume":"19","author":"RJ Woodham","year":"1980","unstructured":"Woodham, R.J.: Photometric method for determining surface orientation from multiple images. Opt. Eng. 19(1), 134\u2013144 (1980)","journal-title":"Opt. Eng."},{"issue":"12","key":"636_CR82","doi-asserted-by":"crossref","first-page":"1250","DOI":"10.1109\/34.817406","volume":"21","author":"P Worthington","year":"1999","unstructured":"Worthington, P., Hancock, E.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. Pattern Anal. Mach. Intell. 21(12), 1250\u20131267 (1999)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"636_CR83","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11263-009-0207-3","volume":"86","author":"C Wu","year":"2010","unstructured":"Wu, C., Narasimhan, S., Jaramaz, B.: A multi-image shape-from-shading framework for near-lighting perspective endoscopes. Int. J. Comput. Vis. 86, 211\u2013228 (2010)","journal-title":"Int. J. Comput. Vis."},{"key":"636_CR84","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1007\/s11263-009-0222-4","volume":"86","author":"KJ Yoon","year":"2010","unstructured":"Yoon, K.J., Prados, E., Sturm, P.: Joint estimation of shape and reflectance using multiple images with known illumination conditions. Int. J. Comput. Vis. 86, 192\u2013210 (2010)","journal-title":"Int. J. Comput. Vis."},{"issue":"8","key":"636_CR85","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1109\/34.784284","volume":"21","author":"R Zhang","year":"1999","unstructured":"Zhang, R., Tsai, P.S., Cryer, J., Shah, M.: Shape from shading: a survey. IEEE Trans. Pattern Anal. Mach. Intell. 21(8), 690\u2013706 (1999)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"636_CR86","doi-asserted-by":"crossref","unstructured":"Zheng, Q., Chellappa, R.: Estimation of illuminant direction, albedo, and shape from shading. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991. Proceedings CVPR \u201991. pp. 540\u2013545 (1991)","DOI":"10.1109\/CVPR.1991.139750"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-016-0636-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-016-0636-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-016-0636-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T10:34:45Z","timestamp":1748774085000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-016-0636-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,10]]},"references-count":86,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["636"],"URL":"https:\/\/doi.org\/10.1007\/s10851-016-0636-x","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"type":"print","value":"0924-9907"},{"type":"electronic","value":"1573-7683"}],"subject":[],"published":{"date-parts":[[2016,2,10]]}}}