A novel RANSAC approach to robustly solve the 3D similarity transformation problem

A novel RANSAC robust estimation technique is presented as an effiecient method for solving the seven-parameter datum transformation problem in the presence of outliers. RANSAC method, which is frequently employed in geodesy, has two sensitive features: (i) the user adjusts some parameters of the algorithm, making it subjective and a rather difficult procedure, and (ii) in its shell, a nonlinear system of equation should be solved repeatedly. In this contribution, we suggest an automatic adjustment strategy for the most important parameter, ‘the threshold value’, based on the ‘early stopping’ principle of the machine-learning technology. Instead of using iterative numerical methods, we propose the use of an algebraic polynomial system developed via a dual-quaternion technique and solved by a non-iterative homotophy method, thereby reducing the computation time considerably. The novelty of the proposed approach lies in three major contributions: (i) the provision for automatically finding the proper error limit parameter for RANSAC method, which has until now been a trial-and-error technique; (ii) employing the algebraic polynomial form of the dual-quaternion solution in the RANSAC shell, thereby accelerating the repeatedly requested solution process; and (iii) avoiding iterations via a heuristic approach of the scaling parameter. To illustrate the proposed method, the transformation parameters of the Western Australian Geodetic Datum (AGD 84) to Geocentric Datum Australia (GDA 94) are computed.