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In this paper we present a novel mathematical model for color image processing. The proposed algebraic structure is based on a special mapping of color vectors into the space of bi-quaternions (quaternions with complex coefficients) inspired by the theory of relativity. By this transformation, the space of color vectors remains closed under scalar multiplication and addition and limited by upper and lower bounds. The proposed approach is therefore termed Caged Image Processing (KIP). We demonstrate the usability of the new model by a color image enhancement algorithm. The proposed enhancement algorithm prevents information loss caused by over saturation of color, caused when using Logarithmic Image Processing (LIP) approach. Experimental results on synthetic and natural images comparing the proposed algorithm to the LIP based algorithm are provided.