@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {127--138},
publisher = {Dunod},
address = {Paris},
volume = {34},
number = {1},
year = {2000},
zbl = {0973.35017},
mrnumber = {1735973},
language = {en},
url = {http://archive.numdam.org/item/M2AN_2000__34_1_127_0/}
}
TY - JOUR AU - Barnes, Ian AU - Zhang, Kewei TI - Instability of the eikonal equation and shape from shading JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique PY - 2000 DA - 2000/// SP - 127 EP - 138 VL - 34 IS - 1 PB - Dunod PP - Paris UR - http://archive.numdam.org/item/M2AN_2000__34_1_127_0/ UR - https://zbmath.org/?q=an%3A0973.35017 UR - https://www.ams.org/mathscinet-getitem?mr=1735973 LA - en ID - M2AN_2000__34_1_127_0 ER -
Barnes, Ian; Zhang, Kewei. Instability of the eikonal equation and shape from shading. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 1, pp. 127-138. http://archive.numdam.org/item/M2AN_2000__34_1_127_0/
[1] , Sobolev Space. Academic Press New York (1975). | MR 450957 | Zbl 0314.46030
[2] , A version of the fundamental theorem for Young measure. Lect. Notes Phys. Springer Verlag 344 (1988) 207-215. | MR 1036070 | Zbl 0991.49500
[3] , results applicable to computer vision. J. Math. Phys. 23 (1982) 890-896. | MR 655907 | Zbl 0502.35079
[4] and , On shape from shading problem Functional Analysis, Approximation Theory and Numerical Analysis, J.M. Rassias Ed., World Scientific (1994) 93-105. | MR 1298653 | Zbl 0878.35026
[5] Direct Methods in the Calculus of Variations. Springer-Verlag (1989). | MR 990890 | Zbl 0703.49001
[6] and , Some remarks on the shape-from-shading problem in computer vision. J. Math. Anal. Appl. 84 (1981) 235-248. | MR 639534 | Zbl 0485.35081
[7] and , Measure Theory and Fine Properties of Functions. Stud. in Adv. Math. CRC Press, Boca Raton (1992). | MR 1158660 | Zbl 0804.28001
[8] and , Analyse convexe et problèmes variationnels. Dunod Paris (1974). | MR 463993 | Zbl 0281.49001
[9] , Blue Moon Rendering Tools: Ray tracing software available from ftp://ftp.gwu.edu/pub/graphics/BMRT (1995).
[10] , Robot Vision. Engineering and Computer Science Series, MIT Press, Mac Graw Hill (1986).
[11] and , Shape from Shading. Ed. MIT Press Ser. in Artificial Intelligence (1989). | MR 1062877
[12] and , Variational Approach to Shape from Shading in [11].
[13] , and , Geomview Visualisation software available from ftp.geom.umn.edu or http://www.geom.umn.edu/locate/geomview.
[14] , and , Shape-from-shading, viscosity solutions and edges. Numer. Math. 64 (1993) 323-353. | MR 1206667 | Zbl 0804.68160
[15] , The RenderMan Interface, version 3.1, official specification. Pixar (1989).
[16] , and , Geomview: An Interactive Geometry Viewer. Notices Amer. Math. Soc. 40 (1993) 985-988.
[17] and , A viscosity solution approach to shape-from-shading. SIAM J. Numer. Anal. 29 (1992) 867-884. | MR 1163361 | Zbl 0754.65069
[18] , Singular Integrals and Differentiability Properties of Functions. Princeton University Press (1970). | MR 290095 | Zbl 0207.13501
[19] , Compensated compactness and partial differential equations, in Microstructure and Phase Transitions, D. Kinderlehrer et al. Eds., Springer Verlag (1992).
