EXTRACTING STRUCTURE FROM AN AFFINE VIEW OF A 3D POINT SET WITH ONE OR 2 BILATERAL SYMMETRIES

We demonstrate that the structure of a 3D point set with a single bila teral symmetry can be reconstructed from an uncalibrated affine image, modulo a Euclidean transformation, up to a four parameter family of s ymmetric objects that could have given rise to the image. If the objec t has two orthogonal bilateral symmetries, its shape can be reconstruc ted, modulo a Euclidean transformation, to a three parameter family of symmetric shapes that could have given rise to the image. Furthermore , if the camera aspects ratio is known, the three parameter family red uces to a single scale and the orientation of the object can be determ ined. These results are demonstrated using real images with uncalibrat ed cameras.