@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/} }
TY - JOUR AU - Barnes, Ian AU - Zhang, Kewei TI - Instability of the eikonal equation and shape from shading JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2000 SP - 127 EP - 138 VL - 34 IS - 1 PB - Dunod PP - Paris UR - http://www.numdam.org/item/M2AN_2000__34_1_127_0/ LA - en ID - M2AN_2000__34_1_127_0 ER -
%0 Journal Article %A Barnes, Ian %A Zhang, Kewei %T Instability of the eikonal equation and shape from shading %J ESAIM: Modélisation mathématique et analyse numérique %D 2000 %P 127-138 %V 34 %N 1 %I Dunod %C Paris %U http://www.numdam.org/item/M2AN_2000__34_1_127_0/ %G en %F M2AN_2000__34_1_127_0
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] Sobolev Space. Academic Press New York (1975). | MR | Zbl
,[2] A version of the fundamental theorem for Young measure. Lect. Notes Phys. Springer Verlag 344 (1988) 207-215. | MR | Zbl
,[3] results applicable to computer vision. J. Math. Phys. 23 (1982) 890-896. | MR | Zbl
,[4] On shape from shading problem Functional Analysis, Approximation Theory and Numerical Analysis, J.M. Rassias Ed., World Scientific (1994) 93-105. | MR | Zbl
and ,[5] Direct Methods in the Calculus of Variations. Springer-Verlag (1989). | MR | Zbl
[6] Some remarks on the shape-from-shading problem in computer vision. J. Math. Anal. Appl. 84 (1981) 235-248. | MR | Zbl
and ,[7] Measure Theory and Fine Properties of Functions. Stud. in Adv. Math. CRC Press, Boca Raton (1992). | MR | Zbl
and ,[8] Analyse convexe et problèmes variationnels. Dunod Paris (1974). | MR | Zbl
and ,[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] Shape from Shading. Ed. MIT Press Ser. in Artificial Intelligence (1989). | MR
and ,[12] Variational Approach to Shape from Shading in [11].
and ,[13] Geomview Visualisation software available from ftp.geom.umn.edu or http://www.geom.umn.edu/locate/geomview.
, and ,[14] Shape-from-shading, viscosity solutions and edges. Numer. Math. 64 (1993) 323-353. | MR | Zbl
, and ,[15] The RenderMan Interface, version 3.1, official specification. Pixar (1989).
,[16] Geomview: An Interactive Geometry Viewer. Notices Amer. Math. Soc. 40 (1993) 985-988.
, and ,[17] A viscosity solution approach to shape-from-shading. SIAM J. Numer. Anal. 29 (1992) 867-884. | MR | Zbl
and ,[18] Singular Integrals and Differentiability Properties of Functions. Princeton University Press (1970). | MR | Zbl
,[19] Compensated compactness and partial differential equations, in Microstructure and Phase Transitions, D. Kinderlehrer et al. Eds., Springer Verlag (1992).
,