Instability of the eikonal equation and shape from shading
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 127-138. 
@article{M2AN_2000__34_1_127_0,
     author = {Barnes, Ian and Zhang, Kewei},
     title = {Instability of the eikonal equation and shape from shading},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {127--138},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {1},
     year = {2000},
     mrnumber = {1735973},
     zbl = {0973.35017},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_1_127_0/}
}
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Barnes, Ian; Zhang, Kewei. Instability of the eikonal equation and shape from shading. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 127-138. http://www.numdam.org/item/M2AN_2000__34_1_127_0/

[1] R.A. Adams, Sobolev Space. Academic Press New York (1975). | MR | Zbl

[2] J.M. Ball, A version of the fundamental theorem for Young measure. Lect. Notes Phys. Springer Verlag 344 (1988) 207-215. | MR | Zbl

[3] A.R. Bruss, results applicable to computer vision. J. Math. Phys. 23 (1982) 890-896. | MR | Zbl

[4] J. Chabrowski and K.-W. Zhang, On shape from shading problem Functional Analysis, Approximation Theory and Numerical Analysis, J.M. Rassias Ed., World Scientific (1994) 93-105. | MR | Zbl

[5] B. Dacorogna Direct Methods in the Calculus of Variations. Springer-Verlag (1989). | MR | Zbl

[6] P. Deift and J. Sylvester, Some remarks on the shape-from-shading problem in computer vision. J. Math. Anal. Appl. 84 (1981) 235-248. | MR | Zbl

[7] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Stud. in Adv. Math. CRC Press, Boca Raton (1992). | MR | Zbl

[8] I. Ekeland and R. Temam, Analyse convexe et problèmes variationnels. Dunod Paris (1974). | MR | Zbl

[9] L. Gritz, Blue Moon Rendering Tools: Ray tracing software available from ftp://ftp.gwu.edu/pub/graphics/BMRT (1995).

[10] B.K.P. Horn, Robot Vision. Engineering and Computer Science Series, MIT Press, Mac Graw Hill (1986).

[11] B.K.P. Horn and M.J. Brooks, Shape from Shading. Ed. MIT Press Ser. in Artificial Intelligence (1989). | MR

[12] B.K.P. Horn and M.J. Brooks, Variational Approach to Shape from Shading in [11].

[13] S. Levy, T. Munzner and M. Phillips, Geomview Visualisation software available from ftp.geom.umn.edu or http://www.geom.umn.edu/locate/geomview.

[14] P.-L. Lions, E. Rouy and A. Tourin, Shape-from-shading, viscosity solutions and edges. Numer. Math. 64 (1993) 323-353. | MR | Zbl

[15] Pixar, The RenderMan Interface, version 3.1, official specification. Pixar (1989).

[16] M. Phillips, S. Levy and T. Munzner, Geomview: An Interactive Geometry Viewer. Notices Amer. Math. Soc. 40 (1993) 985-988.

[17] E. Rouy and A. Tourin, A viscosity solution approach to shape-from-shading. SIAM J. Numer. Anal. 29 (1992) 867-884. | MR | Zbl

[18] E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press (1970). | MR | Zbl

[19] L. Tartar, Compensated compactness and partial differential equations, in Microstructure and Phase Transitions, D. Kinderlehrer et al. Eds., Springer Verlag (1992).