Inference of 3-D shape with edge from image brightness

A traditional method to reconstruct a 3-D shape from shading is to structure an objective functional H(X), over surface normal distribution X, which is a weighted average of the regularization terms representing smoothness constraints and data term representing the image-irradiance equation; the reconstruction is then to find the surface normal distribution X, which minimizes H. However, there is a prominent weakness in that it is difficult to recover discontinuities in the surface normal at edges. In order to overcome this drawback, we propose a new method of shape from shading by using a concave-type regularization term for reconstruction of a 3-D shape with edges for non-Lambertian surface. We theoretically prove that the algorithm is convergent and effective for recovery of a 3-D shape with edges. We also provide experimental comparison of the proposed method with the existing method by using both numerical and real images. Experimental results show that our recovery is more accurate.