Solving a similarity transformation between two reference frames using hybrid geometric control features

Abstract

A similarity-based transformation has been routinely applied in various fields of geosciences with the main purpose of integrating spatial information across different reference frames. Current approaches for solving the indirect problem (i.e., parameter estimation) of a similarity transformation are primarily point-based approaches, meaning that point correspondence between the original and transformed frames (namely control points) is required. Although it can also be seen that transformation solutions have been reached by means of other features, they have been mainly presented on the basis of a single feature, or, at most a few features, thus exploiting only limited geometric information inside the data. In this study, an integrated technique for solving the transformation parameters is developed using not only point features but also linear and planar features and clusters of point clouds with implicit or explicit features. In addition, this approach provides a closed-form solution for a transformation and, consequently, does not require an appropriate starting value to initiate the transformation parameter estimation. An illustration is given in numerical tests of how the proposed approach is able to process various kinds of control features and gives a reliable result with high computational efficiency. Accordingly, a flexible and automatic determination of a 3-D similarity transformation can be achieved by implementing this technique. Potential applications include geodetic datum transformations, reference analysis of LiDAR point clouds, extraction of features from LiDAR surveying or satellite image data, and registration of digital vector maps in GIS.