A Practical Quality Index for the Applied Helmert Transformation

Abstract

The Helmert transformation is used in different procedures in geodesy, photogrammetry, and in general in geomatics. The assessment of the accuracy of the transformation, and in particular of the transformed coordinates, is often critical. In this paper, a new overall quality index describing the accuracy of the transformed points is proposed. This index was derived from the spectral radius of the variance-covariance matrix of the transformed coordinates by writing an expression that represents an upper bound of this quantity. The proposed index is fast to compute and expresses the extent of the uncertainty propagation in a clear and synthetic way. The paper presents the rationale behind the choice of the index and the algebraic steps for its computation. Finally, two examples, one using synthetic data and one involving the coregistration of a point cloud acquired with a laser scanner, are presented.