Use of generalised Procrustes analysis for the photogrammetric block adjustment by independent models

Abstract

The paper reviews at first some aspects of the generalised Procrustes analysis (GP) and outlines the analogies with the block adjustment by independent models. On this basis, an innovative solution of the block adjustment problem by Procrustes algorithms and the related computer program implementation are presented and discussed. The main advantage of the new proposed method is that it avoids the conventional least squares solution. For this reason, linearisation algorithms and the knowledge of a priori approximate values for the unknown parameters are not required. Once the model coordinates of the tie points are available and at least three control points are known, the Procrustes algorithms can directly provide, without further information, the tie point ground coordinates and the exterior orientation parameters. Furthermore, some numerical block adjustment solutions obtained by the new method in different areas of North Italy are compared to the conventional solution. The very simple data input process, the less memory requirements, the low computing time and the same level of accuracy that characterise the new algorithm with respect to a conventional one are verified with these tests. A block adjustment of 11 models, with 44 tie points and 14 control points, takes just a few seconds on an Intel PIII 400 MHz computer, and the total data memory required is less than twice the allocated space for the input data. This is because most of the computations are carried out on data matrices of limited size, typically 3×3.