Open AccessTHREE-DIMENSIONAL TRANSFORMATION OF COORDINATE SYSTEMS USING NONLINEAR ANALYSIS – PROCRUSTES ALGORITHM
Author(s) -
Valeria Ersilia Oniga Corina Daniela Păun *
Publication year - 2017
Publication title -
zenodo (cern european organization for nuclear research)
Language(s) - English
DOI - 10.5281/zenodo.291839
Subject(s) - algorithm , procrustes analysis , transformation (genetics) , nonlinear system , mathematics , computer science , coordinate system , artificial intelligence , physics , chemistry , biochemistry , quantum mechanics , gene
The coordinates transformation between two projection systems is increasingly approached in geodesy, photogrammetry and computer vision. This issue led to widespread development of algorithms that offer high accuracy and fast processing time. One of this algorithms was presented in this paper, namely the Procrustes algorithm, which involves the usage of seven parameters of transformation (three of translation, three of rotation and one scalar). The main advantages of this algorithm is that you don’t have to know the initial values of the parameters, like in the case of iterative numerical methods and the process of equations linearization in order to obtain the equation correction system, isn’t necessary. So, to the standard equation of 3D- transformation, the Lagrange function is applied, together with some constraints on rotation matrix (R must be orthogonal) and some derivation conditions. In order to obtain more accurate results in the 3D transformation of coordinates the weights matrix is introduced, which is calculated separately based on variance-covariance matrix, using the error matrix. This paper also investigates the stability of using this algorithm for the registration of two TLS point clouds, by comparing the results with those obtained by applying the 3D conformal transformation. When using the last algorithm, the initial values of the 7- parameters were calculated and an iterative optimization of these parameters was applied