Motion and structure from point correspondences with error estimation: planar surfaces

The determination of motion and structure of a planar scene from monocular image sequences, is studied. A new and simpler linear algorithm, that gives closed-form solutions for motion and structure parameters using point correspondences between two images, assuming that the coplanar points undergo a rigid motion in 3-D space, is presented. A series of analytical results is established. From two perspective views of a planar scene which is undergoing a rigid motion, there are generally two (normalized) interpretations for motion parameters and the positions of the object plane. These two interpretations, one vertical and the other illusive, are both valid in the sense that they render the same pair of images. The authors identify all the special cases in which the number of interpretations is not two, and derive necessary and sufficient geometrical conditions for those special cases to occur. The approach to error estimation is based on the first-order perturbation. The estimated errors provide quantitative assessment for the accuracy of the solutions. They also indicate degenerate or nearly degenerate configurations in the presence of noise