This paper presents a practical method that estimates illumination distribution from shadows where the shadows are assumed to be cast on a textured, Lambertian surface. Previous methods usually require that the reflectance property of the surface be constant or uniform, or need an additional image to cancel out the effects of varying albedo of the textured surface. We deal with an estimation problem for which surface albedo information is not available. In this case, the estimation problem corresponds to an underdetermined one. We show that combination of regularization by correlation and some user-specified information can be a practical method for solving the problem. In addition, as an optimization tool for solving the problem, we develop a constrained Non-Negative Quadratic Programming (NNQP) technique into which not only regularization but also user-specified information are easily incorporated. We test and validate our method on both synthetic and real images and present some experimental results.