There are many objects in the real world, especially, man made objects often having a polyhedral shape. Shape
from shading (SFS) is a well known and the most robust technique of Computer vision. SFS is a first order
nonlinear, ill-posed problem. The main idea for solving ill-posed problems is to restrict the class of admissible
solution by introducing suitable a priori knowledge. To overcome the ill-posedness in SFS techniques, Bayesian
estimation of geometrical constraints are used. The Lambertian reflectance model is used in this method due to
its wide applicability in SFS techniques. The priori or the constraints are represented in the form of probability
distribution function, so that the Bayesian approach can be applied. The Monte Carlo method is applied
for generating the sample fields from the distribution so that the model can represent our priori knowledge and
constraints. The optimal estimators are also computed by using Monte Carlo method. The geometric constraints
for lines and planes are used in probabilistic manner to eliminate the rank deficiency to get the unique solution.
In case of incorrect line drawings, it is not always possible to reconstruct the object shape uniquely. To deal with
this problem, we have processed each planar face separately. Hence, the proposed method is applicable in case
of slight error in computation of vertex positions in the images of polyhedral objects. The proposed method is
used on various synthetic and real images and satisfactory results are obtained.