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.

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