Colour is modelled using a Lie group using space-time metric. The use of the split quanternion algebra is a new venue of promising research for color image processing. As opposite to current works which use RGB images in the Euclidean Vector space, we modell the colour HSV using the null cone. For the processing, we developed the Quaternion Split Fast Fourier Transform and show also the new concepts of filtering and image enhancement in the space-time metric. In addition, we developed a new method to interpolate color images using G_{3,1}. An experimental analysis with every day color images is presented