Bundle adjustment

Overview

Bundle block adjustment (BBA) estimates the tie-point positions, the camera exterior orientations and the camera calibration together, and fixes the result to survey coordinates with ground control points (GCPs) [arxiv:2610.01438 §2.2] tab. 1. Its accuracy is judged on separate check points (CPs), which are measured once and kept out of the adjustment 2610.01438 §2.1 §2.3.

The invariant that all variants share is the input: the same images, the same GCP and CP measurements, and the same software. Only the adjustment settings change 2610.01438 §2.1. The paper's motivation is that photogrammetry software is often run as a black box with its defaults, and that the BBA settings are rarely studied 2610.01438 §1.

The paper's full-factorial study ran 768 setting combinations on ten UAV surveys of one 220 ha site at 10 mm ground sampling distance. The best 10 % of variants reached 15.9 to 19.8 mm mean 3D error at the CPs, and the worst 10 % reached 64.8 to 303.4 mm 2610.01438 §3.1. These are results for one software package and one site, and the authors tie their conclusions to those conditions 2610.01438 §1.

Variants

Each factor below is a setting, not a separate algorithm. The paper gives the levels and the effect of each level on the errors 2610.01438 §2.2 tab. 1 tab. 2. All of it comes from the paper's card, The Impact of Processing Parameters on High-Accuracy Measurements in UAV Photogrammetry.

Ground control points (NGCP, GCPA)

• NGCP is 1, 5, 9 or 23 GCPs. Added points do not move the earlier ones 2610.01438 §2.2. With one GCP, the mean elevation error is 54.9 mm; with 5 it is 9.7 mm, and with 23 it is 1.7 mm 2610.01438 tab. 2.
• GCPA is the assumed accuracy of each GCP coordinate, 25 mm or 15 mm 2610.01438 §2.2. The 15 mm setting gave lower mean elevation error (14.2 mm against 21.9 mm) 2610.01438 tab. 2. The top-10 % subset contains no single-GCP variant 2610.01438 §3.1 tab. 4.

Camera-position source (PCMD, PCA)

• PCMD fixes the projection centres either by RTN (virtual reference stations from a service) or by PPK (a static base station on site, baseline under 1 km) 2610.01438 §2.2. The PPK mean elevation error was 14.9 mm against 21.2 mm for RTN 2610.01438 tab. 2. PPK was used in more than 90 % of the top-10 % variants 2610.01438 §3.1.
• PCA is the a priori accuracy of the camera centres: 100 mm, 50 mm, or "estimated" from the PPK or RTN processing 2610.01438 §2.2. The paper does not give a numeric value for "estimated" 2610.01438 §2.2. The estimated setting gave the lowest mean elevation error of the three 2610.01438 tab. 2.

Self-calibration (AC)

AC switches on additional correction terms, a 96-parameter model from Tang et al. fitted on top of Brown's calibration model 2610.01438 §2.2. Mean elevation error was 29.6 mm with AC off and 6.6 mm with AC on [arxiv:2610.01438 tab. 2]. Every top-10 % variant had AC on, and the worst 10 % were dominated by AC off 2610.01438 §3.1 fig. 4.

Tie points (TPA, TPF)

• TPA is the tie-point accuracy, 1 px or 2 px 2610.01438 §2.2. The 2 px setting gave lower mean elevation error (10.5 mm against 25.7 mm) 2610.01438 tab. 2. Over 70 % of top-10 % variants used 2 px 2610.01438 §3.1.
• TPF is an optional tie-point filter. It removes points seen in fewer than 3 images, or with reconstruction uncertainty or projection accuracy above 8. It then re-adjusts and removes points with reprojection error above 0.25 until the maximum is below 0.5. The thresholds are unitless and specific to Metashape 2610.01438 fig. 2. Its effect on mean elevation error is 23.7 mm without and 12.5 mm with 2610.01438 tab. 2. Its effect among the best variants is disputed; see Contradictions.

Post-adjustment transform (TR)

TR applies a seven-parameter similarity transform (three translations, three rotations, one scale) after the final BBA 2610.01438 §2.2. Without it, the mean along-track error was -1.3 mm; with it, 2.0 mm, and mean elevation error fell from 24.6 mm to 11.5 mm 2610.01438 tab. 2. Over 70 % of top-10 % variants used a transform 2610.01438 §3.1.

When to use which

The paper's results come from one site, one software package and a GSD of 10 mm. Treat the rows below as the paper's evidence, not as general rules.

Implementation sketch

The common core is one adjustment, run on the same inputs for every variant. Where variants differ, the step is marked. The paper does not say how tie points are rebuilt after images are removed; the sketch keeps the surviving points, which is an assumption 2610.01438 §2.2.

# One BBA variant on one series [arxiv:2610.01438 §2.2]
# Input: images, GCP and CP coordinates, one setting per factor

def run_variant(images, gcps, cps, setting):
    # Align images: 40,000 keypoints, 10,000 tie points each [§2.2]
    tie_points = align_images(images, 40000, 10000)
    # Trial BBA: AC off, TPA 1 px, PCA estimated, TPF off [§2.2]
    trial = bba(tie_points, gcps, TRIAL_SETTINGS)
    # Drop images with clearly wrong orientation, under 1 % [§2.2]
    images = drop_gross_errors(images, trial)
    # Keep surviving points; paper does not say how [§2.2]
    tie_points = keep_points_of(tie_points, images)
    # Variant step: optional tie-point filter (TPF) [fig. 2]
    if setting.tpf:
        tie_points = filter_tie_points(tie_points, gcps, setting)
    # Final BBA with the variant's own settings [§2.2]
    adjustment = bba(tie_points, gcps, setting)
    # Variant step: optional seven-parameter transform (TR) [§2.2]
    if setting.tr:
        adjustment = similarity_transform(adjustment, gcps)
    # Rank by mean 3D error at the check points [§2.3]
    return rmse_3d(adjustment, cps)

Contradictions

• Within the paper: TPF among the best variants. The text says TPF has no significant effect on the best variants, and the enhanced configuration turns it off 2610.01438 §3.2. The top-10 % table gives a Bartlett p-value of 0.231 for the along-track spread, but 0.000 for the across-track spread and 0.001 for the elevation spread 2610.01438 tab. 4. The text does not reconcile these. On all variants, TPF changes mean elevation error from 23.7 mm to 12.5 mm 2610.01438 tab. 2.
• Within the paper: study area. The methods give 220 ha [arxiv:2610.01438 §2.1]; the discussion gives 200 ha 2610.01438 §4. The card and this page use 220 ha.
• Across papers. None known. This page has one source.

Papers

• The Impact of Processing Parameters on High-Accuracy Measurements in UAV Photogrammetry: a full-factorial study of eight BBA settings in Agisoft Metashape on ten UAV surveys, with the effect of each setting on check-point and deformation error.