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The Logarithmic Image Processing (LIP) approach is a mathematical framework developed for the representation and processing of images valued in a bounded intensity range. The LIP theory is physically and psychophysically well justified since it is consistent with several laws of human brightness perception and with the multiplicative image formation model. In this paper, the so-called Color Logarithmic Image Processing (CoLIP) framework is introduced. This novel framework expands the LIP theory to color images in the context of the human color visual perception. Color images are represented by their color tone functions that can be combined by means of basic operations, addition, scalar multiplication and subtraction, opening new pathways for color image processing. In order to highlight the CoLIP relevance with color constancy, a color correction method based on the subtraction is proposed and tested on CoLIP approach and Logarithmic hUe eXtension (LUX) approach, also based on the LIP theory, on differently illuminated images: underwater images with a blue illuminant, and indoor images with yellow illuminant.