Structure from Motion: Theoretical Foundations of a Novel Approach Using Custom Built Invariants

We rephrase the problem of 3D reconstruction from images in terms of intersections of projections of orbits of custom built Lie groups actions. We then use an algorithmic method based on moving frames à la Fels-Olver to obtain a fundamental set of invariants of these groups actions. The invariants are used to define a set of equations to be solved by the points of the 3D object, providing a new technique for recovering 3D structure from motion.