Procrustes Statistics to Test for Significant OLS Similarity Transformation Parameters

  • A. Beinat
  • F. Crosilla
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


Ordinary least squares (OLS) similarity transformations are often used in practice to perform datum conversions in a wide spectrum of geodetic and photogrammetric problems.

Traditionally, the estimation of the unknown parameters is computed by solving a non linear transformation model, build on a set of correspondence point coordinates known in both reference systems.

In the past many efforts have been made to provide a direct OLS solution to the parameter estimation problem. Among the solutions investigated (e.g. Sansò 1973), today very promising results are expected from some algorithms of the Procrustes Analysis (e.g. Crosilla 1999; Grafarend and Awange 2000, 2002).

These methods furnish the mathematical tools to perform a direct similarity transformation parameters estimation between two datums (Ordinary Procrustes Analysis), and among n 2 different datums by an iterative sequence of simultaneous direct solutions (Generalised Procrustes analysis).

In the paper we present a method, inspired to the perturbation theory of the Procrustes Analysis proposed by Langron and Collins (1985), aimed to evaluate the level of significance of the different parameters (translation, rotation and global dilatation) computed by the solution of a classical OLS similarity transformation problem. The procedure has been developed for both the Ordinary Procrustes problem and for the Generalised Procrustes problem.


Procrustes statistics Procrustes analysis OLS similarity transformation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • A. Beinat
    • 1
  • F. Crosilla
    • 1
  1. 1.Department of Georesources and TerritoryUniversity of UdineUdine UDItaly

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