Color Image Processing Using Geometric Algebra

The processing of color images is of great interest because the human perception of color is a very complex process, still not well understood. In this chapter, firstly, the authors present an analysis of the well-known mathematical methods used to model color as a phenomenon and to process color images. We introduce an adequate metric to process color images using the Minkowski or space-time metric.Metric, Minkowski or space-time We propose that the processing of HSV images can be done using the HSV cone in the quaternion split algebra or the conformal geometric algebra frameworks. We show that the processing of RGB images using the Euclidean metric in the \(\mathbb {R}^3\) doesn’t yield good results. The colors of images change by daylight, we understand this phenomenon as the color change follows the action of the Lorentz Lie group. Consequently, we formulate a new model for representing and processing color using split quaternions and space-time conformal geometric algebra. In Chap. 17 , we propose new algorithms for practical color image processing: we formulate the novel split quaternion Fourier transform for color image processing and we interpolate color images using split motors which belong to the space-time conformal geometric algebra.