In shape from shading, iterative algorithms are often used to compute the surface derivatives. These algorithms are, however, very time-consuming when the iterations are performed on the original image. In this paper we propose a multiresolution method which makes use of the orthonormal wavelet transform to construct a multiresolution pyramid and let most iterations be performed on the low resolution images to give good predictions of the initial values of the surface derivatives of higher resolution images and thus save many computations. On the other hand, the nonlinearity of imaging makes the direct reduction of the image resolution not an optimal way of utilizing the multiresolution method. Instead, we construct the pyramid of the norm T= √(p2+q2) of the surface direction (p, q, 1) . We prove that this strategy gives out excellent results when the surface is smooth and the support length of the wavelet is small. Factors that may affect the selection of the wavelet in the multiresolution shape from shading are also studied. Experiments show the superiority of this strategy to other methods.
"Fast shape from shading based on wavelet transform", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); doi: 10.1117/12.170022; https://doi.org/10.1117/12.170022