Color constancy aims to compute object colors despite differences in the color of the light source. Gamut-based approaches are very promising methods to achieve color constancy. In this paper, the gamut mapping approach is extended to incorporate higher-order statistics (derivatives) to estimate the illuminant. A major problem of gamut mapping is that in case of a failure of the diagonal model no solutions are found, and therefore no illuminant estimation is performed. Image value offsets are often used to model deviations from the diagonal model. Prior work which incorporated robustness to offsets for gamut mapping assumed a constant offset over the whole image. In contrast to previous work, we model these offsets to be position dependent, and show that for this case derivative-based gamut mapping yields a valid solution to the illuminant estimation problem. Experiments on both synthetic data and images taken under controlled laboratory settings reveal that the derivativebased and regular gamut mapping methods provide similar performance. However, the derivative-based method outperforms other methods on the more challenging task of color constancy for real-world images.