Different reproduction devices can have different sets of reproducible colours. These sets are called gamuts. The process of transforming colours from one device (or image) gamut to another is called gamut mapping. Gamut mapping has many technical issues to be considered: the used colour space, direction and magnitude of the mapping and whether and to which extent ingamut colours should be altered. Spatially invariant algorithms treat all the pixels independently on their position in the image. Spatially variant (local) algorithms allows a better rendition but introduces the problem of artefacts and/or haloing in the resulting image. In this paper we propose a spatially variant gamut mapping algorithm that creates virtually no artefacts nor haloing in the resulting image. We start from an analysis of the Retinex algorithm and devise proper functionals to build an algorithm which tries to maintain spatial ratios in the image while mapping it into the gamut and, at the same time, avoids all drawbacks of Retinex approaches. We suggest to perform the mapping in an RGB colour space rather than one of the perceptually more homogeneous ones. Although less homogeneous, we experimentally show that RGB colour spaces actually have better hue constancy according to a certain criterion.