Procrustes analysis and geodetic sciences

  • Crosilla F
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Abstract

Procrustes analysis is a well known technique to provide least squares matching of two or more factor loading matrices or for the multidimensional rotation and scaling of different matrix configurations. Applied at first as a useful tool in factor analysis, today it has become a popular method of shape analysis (Goodall 1991, Dryden and Mardia 1998). This paper reviews the development of the most significant algorithms used in this particular field. Starting from the solution of the classical “orthogonal procrustes problem”(Schönemann 1966) a first extension including a scaling factor and a central dilation will be presented (Schönemann and Carroll 1970). The solution of the “generalized orthogonal procrustes problem” to sets of more than two matrices will be then reported (Gower 1975, Ten Berge 1977). Furthermore, “weighted procrustes analysis” will be considered for the cases in which the residuals of a matching procedure are differently weighted across columns (Lissitz et al. 1976) or across rows (Koschat and Swayne 1991) of a matrix configuration . Finally, some possible applications of procrustes methods for point coordinates transformations in geodesy and photogrammetry will be mentioned. All this makes it possible to emphasize the capabilities of the method proposed.

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Authors

  • Fabio Crosilla

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