A unifying framework for color image calibration

In the field of color image calibration, several image transformation models are used, among which the linear model, the affine model, or the quadratic model; we show that the linear algebraic model is the most natural model under the usual assumptions on the image formation and we provide the detailed mathematical justification. Then we examine the different cases derived from this linear algebraic model; we prove that they can be unified in the general framework of constrained least-squares calibration, and show that most of the studies achieved in the field of color image calibration with a reference are particular cases of this general formulation, although they are addressed with different approaches. This allows linking these different methods and deriving predictions on their performances in terms of local and global error.