Direct Solution of the 7 parameters transformation problem

In this paper, we propose a new algorithm to solve the 7 parameters transformation problem. Using Grobner bases techniques and solving polynomial systems, we find, in a direct manner and without the need of a linearization, the values of the translation, rotation and a scale factor. Then, with the aid of simulated data, we will confront the algorithm to all sorts of configurations. Finally, we show the application of this algorithm in photogrammetry.