We present a novel technique for shadow removal based on an information theoretic approach to intrinsic image analysis. Our key observation is that any illumination change in the scene tends to increase the entropy of observed texture intensities. Similarly, the presence of texture in the scene increases the entropy of the illumination function. Consequently, we formulate the separation of an image into texture and illumination components as minimization of entropies of each component. We employ a non-parametric kernel-based quadratic entropy formulation, and present an efficient multi-scale iterative optimization algorithm for minimization of the resulting energy functional. Our technique may be employed either fully automatically, using a proposed learning based method for automatic initialization, or alternatively with small amount of user interaction. As we demonstrate, our method is particularly suitable for aerial images, which consist of either distinctive texture patterns, e.g. building facades, or soft shadows with large diffuse regions, e.g. cloud shadows.