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Shape recovery is a classic problem in computer vision. The goal is to derive a 3-D scene description from one or more 2-D images. The recovered shape can be expressed in several ways: depth Z(x,y), surface normal (nx,ny,nz), surface gradient (p,q), and surface slant, Φ, and tilt, Θ. The depth can be considered either as the relative distance from camera to surface points, or the relative surface height above the x-y plane. The surface normal is the orientation of a vector perpendicular to the tangent plane on the object surface. The surface gradient, (p.q)=(dz/dx, dz/dy), is the rate of change of depth in the x and y directions. The surface slant, Φ, and tilt, Θ, are related to the surface normal as, where l is the magnitude of the surface normal.

Associated publications:
Shape from Shading: A Survey
Ruo Zhang,Ping-Sing Tsai, James Cryer and Mubarak Shah. IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 21, Number 08, August, 1999, pp 690-706.

Shape from Intensity Gradient
Ruo Zhang and Mubarak Shah. IEEE Transactions on Systems, Man and Cybernetics, PART A, May 1999.

From Shape from Shading to Object Recognition
A. Ortega and M. Shah.International Journal of Artificial Intelligence and Pattern recognition, Volume 7, No. 12, November, 1998 pp 969-984.

Shape from Shading with Variable Albedo
Ping-Sing Tsai and Mubarak Shah.Optical Engineering, pp 121-1220, April 1998.

Iterative Shape Recovery From Multiple Images
Ruo Zhang and Mubarak Shah. Image and Vision Computing, Volume 15 (1997), 801-814, November 1997.

Photomtion
Ruo Zhang, Ping-Sing Tsai and Mubarak Shah. CVGIP: Image Understanding, Vol. 63, No. 2, pp 221-231, March 1996.

Shape from Shading and Stereo
James Cryer, Ping-Sing Tsai and Mubarak Shah. Pattern Recognition, Volume 28, No. 7, pp 1033-1043, July 1995.

Shape From Shading Using Linear Approximation
Ping-sing Tsai and Mubarak Shah. Image and Vision Computing Journal, 1994.