Extracting structure from an affine view of a 3D point set with one or two bilateral symmetries

摘要

We demonstrate that the structure of a 3D point set with a single bilateral symmetry can be reconstructed from an uncalibrated affine image, modulo a Euclidean transformation, up to a four parameter family of symmetric objects that could have given rise to the image. If the object has two orthogonal bilateral symmetries, its shape can be reconstructed, 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 reduces to a single scale and the orientation of the object can be determined. These results are demonstrated using real images with uncalibrated cameras.