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Thus a transformation involving 3 full reference points already provides 2 redundant observations. 2) used in industrial metrology, is based on 6 observations, does not derive a scale change, and therefore results in zero redundancy. Approximate values In order to calculate approximate values of the translation and rotation parameters of the similarity transformation, an intermediate coordinate system is formed. This is derived from 3 XYZ reference points P1, P2, P3 as indicated by system uvw (Fig.
This derives an optimal fit between both coordinate systems. 31) Z = Z0 + m( r31 x + r32 y + r33 z ) By linearising the equations at approximate parameter values, corresponding correction equations are built up. Any reference point with defined X,Y and Z coordinates (full reference point) provides three observation equations. Correspondingly, reference points with fewer coordinate components generate fewer observation equations but they can still be used for parameter estimation. Thus a transformation involving 3 full reference points already provides 2 redundant observations.
Further reviews of the history of close range photogrammetry are available in Atkinson (1980), Atkinson (1996), Albertz and Wiedemann (1997), Grün (1994), Karara (1989), Brunner (1988) and von Gruber (1930) and von Gruber et al. (1932). , Ebner, H. and Klein, H. (1970) Ein Rechenprogramm für die Streifentriangulation mit unabhängigen Modellen. Bildmessung und Luftbildwesen, Heft 4/1970, pp. 206–217. Albertz, J. and Wiedemann, A. ) (1997) Architekturphotogrammetrie gestern-heute-morgen. Technische Universität Berlin.