Mirror uncertainty and uniqueness conditions for determining shape and motion from orthographic projection

摘要

This paper presents new forms of necessary and sufficient conditions for determining shape and motion to within a mirror uncertainty from monocular orthographic projections of any number of point trajectories over any number of views. The new forms of conditions use image data only and can therefore be employed in any practical algorithms for shape and motion estimation. We prove that the mirror uncertainty for the three view problem also exists for a long sequence: if shapeS is a solution, so is its mirror imageS′ which is symmetric toS about the image plane. The necessary and sufficient conditions for determining the two sets of solutions are associated with the rank of the measurement matrixW.