We derive a new class of photometric invariants that can be used for a variety of vision tasks including lighting invariant material segmentation, change detection and tracking, as well as material invariant shape recognition. The key idea is the formulation of a scene radiance model for the class of "separable" BRDFs, that can be decomposed into material related terms and object shape and lighting related terms. All the proposed invariants are simple rational functions of the appearance parameters (say, material or shape and lighting). The invariants in this class differ from one another in the number and type of image measurements they require. Most of the invariants in this class need changes in illumination or object position between image acquisitions. The invariants can handle large changes in lighting which pose problems for most existing vision algorithms. We demonstrate the power of these invariants using scenes with complex shapes, materials, textures, shadows and specularities.