Estimates of unknown transformation parameters in terrestrial measurements: one simulated problem

In connection with the expansion of 3D scanners, 3D object modeling has become highly studied in recent years. Many methods are currently available to solve the registration problem, whereby unknown transformation parameters need to be estimated when targeting a 3D object in multiple scans from different locations. Two different problems are encountered in the practice of targeting 3D objects in geodesy or construction. In the first variant, the measurement of the coordinates of the points of the 3D object is realized in several scans on tens of points marked with targets on a reflective surface. In the second variant, measurements of the coordinates of "clouds of hundreds or thousands of points" are available in several scans from different coordinate systems. In clouds it is necessary to find matching pairs of points, called identical points, based on their color match. In both versions, the coordinates of identical points from different coordinate systems must be recalculated to the selected coordinate system during data fusion. The problem leads to finding unknown shift and rotation transformation parameters. The aim of this article is to simulate the measurement of identical points in multiple scans. We will create a test task that can be used to test the methods proposed to solve the registration problem.