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.