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Retinex-based formulations aim at modeling the color perception of an image, and some of them can geometrically be viewed as the averaging of perceptual distances between image pixels. In this talk, I will present a generalization of these distances by considering the parallel transport map associated to a covariant derivative, and from which derives a new variational model for contrast enhancement. I will show some results for well-chosen covariant derivatives that encode brightness perception phenomena.