On 3-D Point Set Matching With MAE and SAE Cost Criteria

This paper deals with the problem of optimally matching two ordered sets of 3-D points by means of a rigid displacement. Contrary to the standard approach, where a sum-of-squared-errors criterion is minimized in order to obtain the optimal displacement, we here analyze the use of [maximum absolute error (MAE)] and [sum of absolute errors (SAE)] cost criteria for determining the optimal matching. Two numerically efficient (polynomial time) algorithms are developed in this paper to compute an approximately optimal solution for the MAE and SAE matching problems.