This doctoral thesis introduces the extension of the LIP (Logarithmic Image Processing) model to color images. The CoLIP (Color Logarithmic Image Processing) model is defined, studied and applied to image processing in this manuscript. 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. Following a study of color vision and color science, the CoLIP model is constructed according to the human color perception stages, while integrating the mathematical framework of the LIP.Initially, the CoLIP is constructed by following the photoreception, non-linear cone compression, and opponent processing human color perception steps. It is developed as a color space representing a color image by a set of three antagonists tones functions, that can be combined by means of specific CoLIP operations: addition, scalar multiplication, and subtraction, which provide to the CoLIP framework a vector space structure. Then, as the CoLIP color space is a luminance-chrominance uniform color space, relative and absolute perception attributes (hue, chroma, colorfulness, brightness, lightness, and saturation) can be defined. Thus, the CoLIP framework combines advantages of a mathematically well structured vector space, and advantages of a color appearance model. In a second step, physical, mathematical, physiological and psychophysical justifications are proposed including a comparison of MacAdam ellipses shapes in the CoLIP uniform model, and in other uniform models, based on ellipses area and eccentricity criterions. Finally, various applications using the CoLIP vector space structure are proposed, such as contrast enhancement, image enhancement and edge detection. Applications using the CoLIP color appearance model structure, defined on hue, brightness and saturation criterions are also proposed. A specific application dedicated to the quantification of viable cells from samples obtained after cytocentrifugation process and coloration is also presented.
