The accurate modeling of the variability of illumination in a class of images is a fundamental problem that occurs in many areas of computer vision and graphics. For instance, in computer vision there is the problem of facial recognition. Simply, one would hope to be able to identify a known face under any illumination. On the other hand, in graphics one could imagine a system that, given an image, the illumination model could be identified and then used to create new images. In this thesis we describe a method for learning the illumination model for a class of images. Once the model is learnt it is then used to render new images of the same class under the new illumination. Results are shown for both synthetic and real images. The key contribution of this work is that images of known objects can be re-illuminated using small patches of image data and relatively simple kernel regression models. Additionally, our approach does not require any knowledge of the geometry of the class of objects under consideration making it relatively straightforward to implement. As part of this work we will examine existing geometric and image-based re-lighting techniques; give a detailed description of our geometry-free face re-lighting process; present non-linear regression and basis selection with respect to image synthesis; discuss system limitations; and look at possible extensions and future work.