Point clouds repeatability and fast scale factor estimates in free SfM surveying: terrestrial application and empirical approach

Previous experiments highlighted the possible existence of a relation between repeatability of point clouds obtained from Structure-from-Motion photogrammetry (SfM), represented by the standard deviation (𝜎), and the nominal ground sampling distance (GSD). In particular, the empirical relation 3𝜎 ∼ 2.5 GSD was found. For this reason, in-situ tests aimed at studying this relation were carried out. Data from seven surveys carried out in 2018-2022 time span allowed the comparison between 20 pairs of almost contemporary point clouds, generated by means of relative bundle adjustment (BA) without ground control points (GCPs) and then relatively scaled and aligned. In this way, the relation 3𝜎 = aGSD was found, where a = 2.5 ± 0.4. This result also suggested the use of the reverse procedure, where the scale factor (SF) is estimated from the standard deviation of non-metric point clouds, 𝜎nmu, by using the relation SFa = aGSD/3𝜎nmu. Additional checks proved that SFa differs from SF by 3%. This error is not acceptable error for length, area or volume measurements, but the estimated SFa is more than adequate for a fast, rough registration of photogrammetric models aimed at searching patterns or precursors of incipient phenomena in impervious/inaccessible areas or in emergency conditions.