Robust surface matching for automated detection of local deformations using least-median-of-squares estimator

Automated detection of the local deformation of a surface involves the detection of the differences between an original and a deformed digital surface model without the aid of control points. The process is normally automated by matching two digital surface models. This technique is desirable for many industrial applications. With the existence of local deformation, conventional surface matching algorithms with least-squares conditions will fail because the estimated parameters are influenced by local deformation. As a result, some robust estimators can be applied to robustify surface matching algorithms. In addition to a re-evaluation of the performance of the M-estimator, two other robust estimators - the GM-estimator and the LMS-estimator (least median of squares) - have been explored in this study for the purpose of detecting local deformation. Test results show that the LMS-estimator is superior to both the M-estimator and the GM-estimator for detecting local deformation in three respects: (1) it is not sensitive to the location of local deformation; (2) the largest tolerable deformation percentage is improved to a level of almost 50 percent; and (3) when the deformation percentage is less than 40 percent, deformations of very small magnitude can be detected. It has also been found that the largest tolerable deformation percentage is related to the magnitude of the deformation.