Abstract
The 3D similarity coordinate transformation is fundamental and frequently encountered in many areas of work such as geodesy, engineering surveying, LIDAR, terrestrial laser scanning, photogrammetry, machine vision, etc. The algorithms of 3D similarity transformation are divided into two categories. One is a closed-form algorithm that is straightforward and fast. However, it cannot provide the accuracy information for the transformation parameters. The other category of algorithm is iterative, and this can offer the accuracy information for the transformation parameters. However, the latter usually needs a good initial value of the unknown. Considering the accuracy information for transformation parameters is essential or indispensable from the viewpoint of uncertainty, this contribution proposes a weighted total least squares (WTLS) iterative algorithm of the 3D similarity coordinate transformation based on Gibbs vectors. It is fast in terms of fewer iterations, reliable and does not need good initial values of transformation parameters. Two cases including the registration of LIDAR points with big rotation angles and a geodetic datum transformation with small rotation angles are demonstrated to validate the new algorithm.
Highlights
The 3D similarity coordinate transformation aims to align the coordinate of points in different coordinate systems into a common coordinate system
This work is very popular in many fields, such as geodesy, engineering surveying, LIDAR, terrestrial laser scanning, photogrammetry, machine vision, etc
This contribution intends to present a new weighted total least squares (WTLS) iterative solution to 3D similarity coordinate transformation based on Gibbs vectors, which is fast and does not need a relatively good initial value of the unknowns; in other words, is not sensitive to the initial value of unknowns
Summary
The 3D similarity coordinate transformation aims to align the coordinate of points in different coordinate systems into a common coordinate system. Felus and Burtch (2009) proposed a closed-form weighted TLS (WTLS) solution to the 3D similarity transformation with pointwise weights and uncorrelated errors among points based on the Procrustes algorithm.
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