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Color constancy is the ability to measure colors of objects independent of the color of the light source. A well-known color constancy method is based on the gray-world assumption which assumes that the average reflectance of surfaces in the world is achromatic. In this paper, we propose a new hypothesis for color constancy namely the gray-edge hypothesis, which assumes that the average edge difference in a scene is achromatic. Based on this hypothesis, we propose an algorithm for color constancy. Contrary to existing color constancy algorithms, which are computed from the zero-order structure of images, our method is based on the derivative structure of images. Furthermore, we propose a framework which unifies a variety of known (gray-world, max-RGB, Minkowski norm) and the newly proposed gray-edge and higher order gray-edge algorithms. The quality of the various instantiations of the framework is tested and compared to the state-of-the-art color constancy methods on two large data sets of images recording objects under a large number of different light sources. The experiments show that the proposed color constancy algorithms obtain comparable results as the state-of-the-art color constancy methods with the merit of being computationally more efficient.