Model based pose estimator using linear-programming

Given a 3D object and some measurements for points in this object, it is desired to find the 3D location of the object. A new model based pose estimator from stereo pairs based on linear programming (LP) is presented. In the presence of outliers, the new LP estimator provides better results than maximum likelihood estimators such as weighted least squares, and is usually almost as good as robust estimators such as least-median-of-squares (LMEDS). In the presence of noise the new LP estimator provides better results than robust estimators such as LMEDS, and is slightly inferior to maximum likelihood estimators such as weighted least squares. In the presence of noise and outliers - especially for wide angle stereo the new estimator provides the best results. The LP estimator is based on correspondence of a points to convex polyhedrons. Each points corresponds to a unique polyhedron, which represents its uncertainty in 3D as computed from the stereo pair. Polyhedron can also be computed for 2D data point by using a-priori depth boundaries. The LP estimator is a single phase (no separate outlier rejection phase) estimator solved by single iteration (no re-weighting), and always converges to the global minimum of its error function. The estimator can be extended to include random sampling and re-weighting within the standard frame work of a linear program.