Shape-from-Shading for Oblique Lighting with Accuracy Enhancement by Light Direction Optimization

We present a shape-from-shading approach for oblique lighting with accuracy enhancement by light direction optimization. Based on an application of the Jacobi iterative method to the consistency between the reflectance map and image, four surface normal approximations are introduced and the resulting four iterative relations are combined as constraints to get an iterative relation. The matrix that converts the shading information to the depth is modified so as to be uniform over the whole image region, making the iteration stable and, as a result, the resulting shape more accurate. Then, to enhance the accuracy, the light direction is optimized for slant angle using two criteria based on the initial boundary value and the rank of the converting matrix. The method is examined using synthetic and real images to show that it is superior to the current state-of-the-art methods and that it is effective for oblique light direction whose slant angle ranges from 55 to 75 degrees.