In this paper, we propose a new algorithm to solve the 7 parameters transformation problem. Using Gr¨obner 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.
Hashemi, Amir; Kalantari, Mahzad; and Kasser, Michel
"Direct Solution of the 7 parameters transformation problem,"
Applied Mathematics & Information Sciences: Vol. 07:
4, Article 15.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss4/15