Optimal Pose Estimation in Two and Three Dimensions

This paper concerns the problem of pose estimation, in particular the application of linear and nonlinear methods to the case of anisotropic error distributions. Incremental and batch techniques are discussed, and a linear solution to the two dimensional problem is developed by reference to the noise model. In this case, manipulation of the normal equations is found to offer a flexible and transparent framework for both techniques. This framework is used to support batch iterative solutions to the 3D imaging problem, and methods are developed that improve the range of stability, the number of iterations, and the computation per iteration each by a factor of about two. Experiments with the batch methods on synthetic data in three dimensions are reported and compared with incremental techniques based on the Kalman filter. The incremental techniques are found to produce significantly suboptimal results and limited stability. For practical applications the computational efficiency of the new batch techniques is found to be better than incremental ones. The techniques are extended to 2D images of 3D data, in the form of single and stereo projections. Experiments with synthetic and real image data show that a suitable choice of anisotropic weighting offers greater accuracy and robustness than perpendicular error measures and examine stereo estimates with and without reconstruction.