A novel approach to structure from motion using custom build invariants

Mireille Boutin

We rephrase the problem of reconstructing an object from a set of pictures in terms of orbits of custom defined Lie group actions. We then use an algorithmic method based on moving frames to obtain a fundamental set of invariants of these group actions. We thus obtain a set of equations to be solved by the points of the 3D object which we can solve numerically. This new, geometric resolution technique is conceptually simple but powerful: e.g., it allows us to deal with the particularly difficult case of a variable focal length. This work is in collaboration with computer scientist P.L. Bazin, SHAPE lab, Brown university.