The paper addresses the problem of ``class-based'' recognition and image-synthesis with varying illumination. The class-based synthesis and recognition tasks are defined as follows: given a single input image of an object, and a sample of images with varying illumination conditions of other objects of the same general class, capture the equivalence relationship (by generation of new images or by invariants) among all images of the object corresponding to new illumination conditions.The key result in our approach is based on a definition of an illumination invariant signature image, we call the "quotient" image, which enables an analytic generation of the image space with varying illumination from a single input image and a very small sample of other objects of the class --- in our experiments as few as two objects. In many cases the recognition results outperform by far conventional methods and the image-synthesis is of remarkable quality considering the size of the database of example images and the mild pre-process required for making the algorithm work.