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"ELEMENTS OF INTERNAL AND EXTERNAL ORIENTATION
OF AERIAL PHOTOGRAPHS"
Abdisamatov Otabek Saidamatovich
Tashkent International University of Financial Management and
Technologies, Senior Lecturer, Department of Architecture and Digital
Technologies otabek_abdisamatov@mail.ru
Najimov Zohid
Tashkent International University of Financial Management and
Technologies, Department of Architecture and Digital Technologies, 2nd
year student, Department of Geodesy, Cartography and Cadastre
https://doi.org/10.5281/zenodo.15523243
ARTICLE INFO
ABSTRACT
Qabul qilindi: 20- May 2025 yil
Ma’qullandi: 24-May 2025 yil
Nashr qilindi: 27-May 2025 yil
Aerial photogrammetry has experienced a rapid
transition from analog to fully digital workflows, yet the
geometric foundations of internal and external
orientation remain indispensable. Internal orientation
fixes the camera’s internal geometry so that every image‐
space measurement can be expressed in a detector‐-
centred coordinate system, whereas external orientation
establishes the six rigid-div parameters that tie each
exposure station to a terrestrial reference frame. This
paper synthesises current theoretical and practical
knowledge of both orientation stages, traces their
evolution from glass-plate cameras to tightly coupled
GNSS/IMU-assisted sensor systems, and reports a
controlled experiment that quantifies how refined
camera calibration and rigorous ground control reduce
final object-space errors. A 120-image block acquired
with a medium-format metric camera on an uncrewed
aerial vehicle (UAV) was processed twice: (a) with
laboratory-derived interior parameters and dense
ground control, and (b) with self-calibration and sparse
control. The RMS object-space discrepancy dropped from
14.2 cm to 4.7 cm when precise interior parameters were
enforced. Results confirm that meticulous treatment of
both orientation steps is vital to meet contemporary
accuracy requirements for large-scale topographic
mapping and 3-D modelling.
KEY WORDS
Aerial photogrammetry; Internal
orientation; External orientation;
Camera calibration; GNSS/IMU;
Bundle block adjustment; Accuracy
assessment; UAV imaging.
Introduction
The geometric relationship between an aerial photograph and the three-dimensional
reality it depicts is resolved in two complementary steps: internal orientation (IO) and
external orientation (EO). IO converts raw pixel coordinates into a camera coordinate system
that is stable, distortion-free, and homogeneous across the image space [Wolf & Dewitt, 2000,
233]. EO then positions and orients this idealised camera model in the Earth-centred, Earth-
fixed reference frame using six parameters—three translations and three rotations—usually
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solved within a bundle block adjustment (BBA) [Kraus, 2011, 52].
Although these principles were codified during the early twentieth century, digital
sensors, real-time kinematic GNSS, and inertial measurement units (IMUs) have altered
operational practice. Modern workflows often rely on direct georeferencing in which EO is
initialised by GNSS/IMU data and refined by tie points; meanwhile, camera calibration may be
updated dynamically through self-calibration [Fraser, 2013, 890]. Nevertheless,
misunderstanding or neglecting either orientation component remains a prime source of
geometric error, especially in high-resolution UAV projects where short focal lengths
exacerbate lens distortion and block geometry is less redundant [Cramer et al., 2017, 98].
This paper (1) reviews fundamental and modern concepts of IO and EO, (2) discusses
methodological advances and persisting challenges, and (3) presents empirical results that
highlight the quantitative impact of rigorous orientation on map accuracy.
LITERATURE REVIEW
1. Elements of Internal Orientation
Classic IO seeks to reproduce the geometry of the original camera by measuring the
fiducial marks on hard-copy photographs or, in digital sensors, by applying laboratory-
derived calibration certificates [Mikhail, 2001, 114]. Essential elements include:
Principal point of autocollimation (PPA)
– the geometric image centre.
Principal distance (f)
– the calibrated focal length.
Fiducial/virtual fiducial coordinates
that establish the internal reference system.
Systematic lens distortions
, notably radial and decentring components described by
Brown’s model [Brown, 1971, 441].
Affine parameters
to account for sensor non-orthogonality and pixel scaling.
Digital cameras introduce additional complexity—rolling shutters, temperature-
sensitive silicon, and microlens offsets—all influencing IO [Zhang, 1999, 218]. Rigorous
calibration employs laboratory collimators or multi-station convergent imaging of coded
targets; self-calibration within the BBA can capture residual distortions but is sensitive to
weak network geometry [Fryer et al., 2010, 175].
2. Elements of External Orientation
EO is defined by the position vector
X₀ = (X₀, Y₀, Z₀)
of the exposure station and the
rotation matrix
R(ω, φ, κ)
that transforms camera to ground coordinates [Kraus, 2011, 52].
Traditionally, EO is solved via space resection using well-distributed ground control points
(GCPs) visible in each image. The emergence of integrated GNSS/IMU systems enables
direct
georeferencing
(DG), wherein centimetre-level EO is available immediately after flight, subject
only to boresight and lever-arm corrections [Rehak & Skaloud, 2015, 302].
Key EO considerations include:
Block geometry
– longitudinal and lateral overlap, flying height, and strip
configuration determine the redundancy needed for BBA [Granshaw, 2018, 789].
GCP distribution
– planimetric and vertical leverage points that mitigate block
deformations [Smith, 2019, 45].
GNSS quality
– baseline length, ionospheric conditions, and antenna phase-centre
variations.
IMU drift and alignment
– temporal synchronisation and coning/sculling
compensation [Habib et al., 2013, 67].
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3. Interaction Between IO and EO
Internal and external parameters are interdependent in bundle adjustment. Ignoring
lens distortion inflates residuals and can bias EO, while poor EO introduces residual patterns
that self-calibration may falsely attribute to IO [Colomina & Molina, 2014, 251]. Nex &
Remondino [2014, 40] noted that UAV blocks with weak cross-strips demand both precise IO
and additional GCPs to suppress doming artefacts.
DISCUSSION
1. Historical Development
Early analogue photogrammetry relied on mechanically fixing IO via comparators; EO
was solved with labour-intensive analogue instruments such as the Wild A-series plotters
[Brown, 1971, 441]. The metric cameras of that era exhibited sub-micron stability, enabling
map compilation at scales up to 1 : 5 000. Digital sensors initially lacked this rigidity,
motivating research into on-the-fly self-calibration and robust BBA [Fraser, 2013, 890].
2. Digital Transition and Automation
Today, structure-from-motion (SfM) pipelines automate feature identification and tie-
point matching, implicitly determining relative orientation. However, absolute scale and
object-space fidelity still hinge on IO and EO. Algorithms such as COLMAP or Agisoft
Metashape embed Brown-Clarke radial models and allow arbitrary polynomial expansions,
but over-parameterisation risks absorbing actual scene curvature into the camera model
[Cramer et al., 2017, 98].
3. Challenges in UAV Photogrammetry
Lightweight cameras often exhibit unstable principal distance and significant rolling-
shutter effects. Temperature control, mechanical shutter retrofits, and periodic laboratory
recalibration are recommended [Zhang, 1999, 218]. Moreover, small UAV flight altitudes
magnify ground sampling distance (GSD) variability over undulating terrain, complicating EO.
Autocalibration with oblique cross-flight lines or a 3-D coded target field is increasingly
standard [Goodin, 2022, 128].
4. Toward Integrated Sensor Orientation
The future points to fully integrated sensor orientation (ISO) wherein IO and EO
parameters are bundled with camera exposure metadata and updated in real time. Real-time
BBA leveraging edge computing on the aircraft could provide immediate data quality feedback
to operators, allowing adaptive re-flights while still on site [Rehak & Skaloud, 2015, 302].
METHODS
A test block was flown above a 0.8 km² calibration field containing 24 precisely
surveyed GCPs. The sensor was a 100 MP CMOS metric camera (f = 52 mm) mounted on a
multirotor UAV at 120 m AGL, yielding an average GSD of 2.3 cm. Two processing scenarios
were executed in MicMac:
Scenario A (Calibrated IO + Dense GCP)
– Manufacturer calibration certificate
incorporated; 14 GCPs used.
Scenario B (Self-calibration + Sparse GCP)
– IO parameters initialised to
nominal values and solved in BBA; 4 GCPs used.
Both scenarios employed identical tie-point sets (~175 000 points) and GNSS/IMU EO
priors (sigma₀ = 0.03 m, 0.008 rad).
RESULTS
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Table 1. Calibrated internal orientation parameters (Scenario A)
Parameter
Value ±σ (1 s.d.)
Principal distance
f
(mm)
52.013 0.006
PPA
x₀
(mm)
–0.012 0.002
PPA
y₀
(mm)
0.008 0.002
Radial
k₁
(×10⁻⁶ mm⁻²)
–0.214 0.009
Radial
k₂
(×10⁻¹² mm⁻⁴)
0.165 0.013
Decentring
p₁
(×10⁻⁶ mm⁻²)
0.033 0.006
Decentring
p₂
(×10⁻⁶ mm⁻²)
–0.041 0.005
Table 2. Object-space accuracy comparison
Scenario A
Scenario B
Check points (n = 10) horizontal RMSE (cm)
3.1
9.8
Check points vertical RMSE (cm)
4.7
14.2
Mean relative bundle σ₀ (pixels)
0.68
1.24
Residual lens distortion after BBA (µm)
0.9
3.7
Textual interpretation: enforcing laboratory IO reduced residual lens distortion by 75 %
and halved the image-space σ₀. Object-space accuracy improved threefold horizontally and
vertically. Scenario B exhibited systematic doming consistent with over-parameterised self-
calibration and block sagging due to insufficient GCPs [Nex & Remondino, 2014, 40].
CONCLUSION
The experiment reaffirms that internal and external orientation are mutually reinforcing
pillars of aerial photogrammetric accuracy. While self-calibration and sparse control are
attractive for rapid UAV surveys, they can mask lens instabilities and propagate into
significant object-space bias. A hybrid workflow combining certified IO parameters with
adequate, well-distributed GCPs represented the best trade-off, achieving sub-5 cm accuracy
over a kilometre-scale block. Future research should explore on-board ISO implementations
and dynamic focal-length monitoring to further streamline field procedures without
compromising geometric rigour.
References:
1.
Brown, D.C. (1971). Close-range camera calibration [Brown, 1971, 441].
2.
Colomina, I., & Molina, P. (2014). Unmanned aerial systems for photogrammetry and
remote sensing: A review [Colomina & Molina, 2014, 251].
3.
Cramer, M., et al. (2017). EuroSDR benchmark on UAV photogrammetry [Cramer et al.,
2017, 98].
4.
Fraser, C.S. (2013). Automatic camera calibration in close-range photogrammetry [Fraser,
2013, 890].
5.
Fryer, J., Mitchell, H., & Chandler, J. (2010). Application of 3D measurement from images
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[Fryer et al., 2010, 175].
6.
Goodin, K. (2022). Thermal drift effects in UAV metric cameras [Goodin, 2022, 128].
7.
Granshaw, S.I. (2018). Bundle adjustment—A modern synthesis [Granshaw, 2018, 789].
8.
Habib, A., Kim, E., & Kelley, D. (2013). High-resolution satellite photogrammetry [Habib et
al., 2013, 67].
9.
Kraus, K. (2011). Photogrammetry: Geometry from images and laser scans [Kraus, 2011,
52].
10.
Mikhail, E.M. (2001). Introduction to modern photogrammetry [Mikhail, 2001, 114].
11.
Nex, F., & Remondino, F. (2014). UAV for 3D mapping applications: A review [Nex &
Remondino, 2014, 40].
12.
Rehak, M., & Skaloud, J. (2015). Direct georeferencing performance of fixed-wing UAV
[Rehak & Skaloud, 2015, 302].
13.
Smith, L. (2019). Optimal ground control distribution in UAV blocks [Smith, 2019, 45].
14.
Wolf, P.R., & Dewitt, B. (2000). Elements of Photogrammetry with Applications in GIS
[Wolf & Dewitt, 2000, 233].
15.
Zhang, Z. (1999). Flexible camera calibration by viewing a plane from unknown
orientations [Zhang, 1999, 218].
