Direct shape reconstruction of 3-D object from monocular shading image

The method described in this paper for reconstructing the shape of Lambertain surfaces from the shading information inherent in a monocular image can deal with a surface whose image (a smooth and non-self-occluding one) is produced by orthographic projection with a parallel light source from a known direction. By dividing the image area into serial triangles, the intensity function I(x,y) on each triangle can be linearized. With the help of a support function and a transformation, it is proved that each triangle represents a cylinder in new X-Y coordinates with (s,t) as its surface gradient components. So, the ill-posed image brightness constraint equation in Cartesian coordinates can be solved in X-Y coordinates with only one variable (either s or t). It is necessary to find out, firstly, the pixel which has the maximal intensity, and then assign its depth leads for the direct recovery of the shape at each point, without the necessity of integration.<>