An algorithm for combining data sets having different frames of reference (Q1315230)

The problem treated by the authors arose from the analysis of hardness tests. In such a test an indenter is driven into a slab of the material under test; the hardness is determined by the diameter of the indentation at the mean surface height of the indent. A frequently used method to find the mean surface height is to use a probe that gives an outline of a 2-D profile of the indent and then use finer instruments to determine more data points near places of large curvature. The problem is that instrument drift, registration error and other factors introduce systematic errors and therefore the data sets cannot simply be merged. In the particular case under consideration, the authors modify the supplementary data sets by applying to each one a translation followed by a homothety. (They note that one could also use an additional rotation.) The parameters for these operations are determined by a Newton approximation for the least squares fit. The main point of the paper are remarks on how to use the block structure of the problem to minimize computational effort. Illustrations are given to show how originally incoherent data sets become coherent after treatment. They point out that their methodology can be used in all cases when data sets for the same object are obtained at different times with different instruments and precisions.