Joint Datum–Form Decomposition for Photogrammetric Acceptance of Large Precision Assemblies

Digital industrial photogrammetry is used for acceptance of large precision assemblies, but separating the time-invariant assembly form error from the epoch-varying measurement perturbation remains challenging. Registering each repeat independently to CAD with a six-degree-of-freedom (6-DoF) datum from only a few control points absorbs part of the form error, biasing the assembly RMS. This article proposes joint datum–form decomposition (JDFD), a generalised Procrustes analysis that shares one CAD-anchored common rigid across repeats and removes each epoch’s residual whole-body similarity. JDFD offers two advantages. First, its assembly RMS is independent of the sparse-control budget: an independent per-epoch 6-DoF overestimates the assembly RMS by ≈43% in Monte Carlo (σM=6.0 μm) and by ≈79% on real data at nc=4 (median ≈ 51% over random layouts), whereas JDFD returns the full-set reference RMS(I^)=11.92 μm at every nc tested. Second, by removing residual similarity, JDFD yields an uncontaminated within-session perturbation RMS(M^)=3.36 μm, compared with 5.57 μm without peeling and 3.91 μm against the full-set independent-datum baseline. The resulting assembly RMS exceeds the 10 μm specification, so acceptance should rest on the nc-invariant RMS(I^).