Shape from shading using wavelets and weighted smoothness constraints

A new method that allows capturing shapes from an input image using an optimisation-based approach is presented. An objective function is designed by introducing two terms: the first term is used to minimise the difference between the shading of the reconstructed shape and the input image, and the second term is to apply smoothness constraints to the reconstructed shape. To achieve shape reconstruction in high quality, the authors propose weighted smoothness constraint, which is designed to be anti-proportional to the intensity gradients in the input image. Under this constraint, flat image areas make more contribution towards the smoothness of the reconstructed shape, while the fine details from the image areas with large intensity gradients are preserved in the reconstructed result. Given the objective function, wavelets are used to obtain the solution effectively. Since wavelets accurately preserve high-frequency data, they can be used to solve the objective function with the advantage of allowing for a good recovery of fine details from the input image. The authors have chosen to use the Daubechies wavelets, which are orthonormal and compactly supported. Here the formulation of the algorithm based on the mathematical details is provided. Finally, the authors present experimental results on a number of different images and compare them against some well-known methods and ground truth (where available). The comparison shows that the method is effective and offers good results.