Shape from shading via the fusion of specular and Lambertian image components

A closed-form analytical solution to the problem of obtaining surface-normal information from the specular and Lambertian components of the image of a surface is presented. It is shown that this algebraic approach to the fusion of data is extremely sensitive to noise, and therefore two alternative approaches based on the minimization of energy functionals are provided. The first approach weights the specular and Lambertian information uniformly over the image with respect to a smoothness constraint. The second approach weights the specular and Lambertian component adaptively according to a measure of the sensitivity of the algebraically derived surface normals to noise in the measured image components. This results in a greater dependence on the smoothness constraint in the parts of the image where the surface reconstruction process is most sensitive to noise and provides a more accurate reconstruction of the surface than the uniform weighting technique