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 Split Quaternion Neural Network in the space-time metric for color image enhancemet. An experimental analysis with every day color images is presented.