Role of Median Curves and Surfaces and Their Computations in Coordinate Metrology

This paper explores a novel role for median curves and surfaces in coordinate metrology, and the techniques to compute these curves and surfaces. The role includes the important problem of identifying potential outliers in two- and three-dimensional geometrical measurements and grouping the measured data into zones of containment without any prejudice to the assumption of underlying probabilistic models. It is shown that using the orthogonal l1-norm in the computation of median curves and surfaces leads to several desirable equivariant and invariant properties. It is also shown that using widely available, free, and open-source software packages renders the task of computing median straight lines, planes, circles, and spheres both easy and efficient. This opens a new avenue for interesting research and industrial applications for coordinate metrology.