Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
Structure from Motion: a New Look from the Point of View of Invariant Theory.
Pierre-Louis Bazin and Mireille Boutin
We present a novel, simple formulation of the problem of 3D object reconstruction from images. In this formulation, the object is seen as lying at the intersection of the projection of orbits of custom-built Lie group actions. The group parameters correspond to unknown, irrelevant quantities such as the camera orientation, the depth parameters of the object with respect to the camera plane and the focal length. We then use an algorithmic method based on moving frames "a la Fels-Olver" to obtain a fundamental set of invariants of these group actions. The invariants are used to define a set of equations detemining the 3D object, thus providing a mathematical formulation of the problem where the irrelevant parameters do not appear.