Rapid, Robust, Optimal Pose Estimation from a Single Affine Image (PREPRINT)

摘要

Determining the rigid transformation relating a 2d image to known geometry is a classical problem in computer vision. To date, the most accurate methods require performing an unknown number of iterations until a numerical algorithm converges to the desired tolerance. For the case of affine imaging, this paper replaces these nonlinear numerical iterations with solving the standard 3d-3d optimal orientation problem 2(n) times, where n is the number of data points. The 2(n) successive optimal orientation calculations are speeded through use of Gray code, and have the dual advantages of speed and predictable execution time. Angular errors caused by scaling imperfections are quantified, and a least upper bound estimate of the scaling is proposed. It is shown that the worst case viewpoints depend only on the data points chosen, and a new convex linear matrix inequality optimization is derived for determining the worst viewpoint. This new analysis tool is useful for evaluating a particular set of data and suggests methods of designing the data for high performance.