Understanding the image coordinate system, applying necessary corrections for finding the coordinate system of image space

1. © 2019 Dr. Sarhat M Adam
BSc in civil Engineering
Msc in Geodetic Surveying
PhD in Engineering Surveying & Space Geodesy
Note – Figures and materials in the slides may be the authors own work or
extracted from internet websites, Materials by Duhok or Nottingham
universities staff and their slides, author's own knowledge, or various internet
image sources and books example (Element of Photogrammetry by wolf).
Lecture 4: Image
measurements &
refinements

2. Introduction
◼ Measurements may be the lengths of lines between imaged points.
◼ Coordinates of imaged points are the most common type of photographic
measurement.
◼ Image coordinates directly used in many photogrammetric Eq.
◼ Coord. Usually made on positives printed on paper, film, or glass, or in
digital images on PC.
◼ Equipment varies from expensive to low cost such as complex machines
that provide computer-compatible digital output to simple scales.
◼ Systematic errors associated with practically all photographic
measurements.
◼ These errors and the manners by which they are eliminated are to be
discussed in this lecture.

3. Coordinate system for image
measurement
◼ Metric camera with F. M., rectangular axis system by joining F. M is
commonly adopted.
◼ The x axis parallel and positive in the direction of flight.
◼ The positive y axis is 90° - from positive x.
◼ The origin of the coordinate system is the intersection of F.M lines.
◼ Position of any image point is given by
its rectangular coordinates xa and ya.
◼ xa is perpendicular distance from y axis
to a.
◼ ya is perpendicular distance from x axis
to a.
◼ Distance ab can be calculated

4. Photographic Measurements from
simple scales
◼ Engineering scale can be used when lower order accuracy is required.
◼ available in both metric and English units and have several different
graduation intervals.
◼ Precision and accuracy can be enhanced by magnifier glass for fine
reading.
◼ For better accuracy, glass scale may be
used.

5. Measuring photo Cordinates
◼ The photo coordinate axis system will be marked first using eng. Scale via
the FM with lines extended using usual 4H pencil.
◼ Perpendicular distances from a points to the formed axis are used to obtain
rectangular coordinates.
◼ The measured coordinates of a point preferred to be sharp and distinctive.
◼ If not, further identification is required with a small pinprick carefully
under magnification.

6. Comparator measurement
◼ Used for film photograph with final coordinate
measurement accuracy.
◼ Comparator able to extract precise photo
coordinates necessary for calibration &
analytical photogrammetry (2 -3) μm.
◼ Are classified nto two basic types
(monocomparators & stereocomparators).
◼ Monocomparators make measurements on one
photograph at a time.
◼ With stereocomparators image positions are
measured by simultaneously viewing an
overlapping stereo pair of photographs
Kern Monocomparator
No longer in use
Stereocomparator by Carl Zeiss, c.
1920

7. Photogrammetric Scanners
◼ Device used to convert analogue to digital.
◼ It is essential that a photogrammetric scanner have sufficient geometric
and radiometric resolution as well as high geometric accuracy.
◼ photogrammetric scanners should be capable of producing digital images
with minimum pixel sizes on the order of 5 to 15 μm.
Leica DSW700 Digital Scanning

8. Refinement of Measured Image
Coordinates
Correction needs to be applied to eliminate or mitigate the systematic
errors from various sources
1. Distortion in focal plane
◼ Film distortions due to shrinkage, expansion, and lack of flatness;
◼ CCD array distortions due to electrical signal timing issues or lack of flatness of the
chip surface
2. Principal point location
◼ Failure of photo coordinate axes to intersect at the principal point;
◼ Failure of principal point to be aligned with centre of CCD array
3. Lens distortions
4. Atmospheric refraction distortions
5. Earth curvature distortion

9. Image Plane Distortion
◼ Shrinkage or expansion present in photograph can be calculated by
comparing the measured distances from fiducial with calibrated FM.
◼ Photo coordinates can be corrected if discrepancies exist.
◼ Depending on necessary level of accuracy, if lower accuracy required
with eng. scale, the following approach is followed:
Where:
xm & ym : measured fiducial distances positive
xc & yc : calibrated fiducial distances positive
x’
a & y’
a : corrected photo coordinates
xa & ya : measured photo coordinates

10. example
For high-accuracy applications, shrinkage or expansion corrections may
be applied through the x and y scale factors of a two-dimensional affine
coordinate transformation.

11. Correction for Lens Distortions
◼ Comprised of two components: symmetric radial distortion & decentring
distortion.
◼ Lens distortions are typically less than 5 μm for modern precision aerial
mapping cameras.
◼ Symmetric radial lens distortion is an unavoidable product of lens
manufacture.
◼ Imperfect assembly of lens elements cause decentring distortion.
◼ Radial lens distortion calculated using the polynomial form
Δr = k1r1+ k2r3+ k3r5+ k4r7
Where Δr = amount of radial lens distortion
r= is the radial distance from the principal point.
k1, k2, k3, k4 = coefficients of the polynomial

12. Correction for Lens Distortions
◼

13. Example

14. Example
◼

15. Least squares example

16. Example

17. Example

18. Correction for Lens Distortions
◼ In modern mapping camera, the lens design evolved to such a level that
symmetric radial and decentring are is of the same order of magnitude.
◼ Simultaneous Multi-camera Analytical Calibration (SMAC) model as an
example is used with USGS calibration procedure.
◼ SMAC computes both distortion parameters in addition to PP & f directly
by LS.
◼ Solved parameters are (k0, k1, k2, k3, k4), (p1, p2, p3, p4), (xp, yp), & f.
Δx, Δy = decentring distortion correc.
r = is the radial distance from the PP.
k0, k1, k2, k3, k4 = coefficients of the
symmetric radial lens distortion
= coordinates of the image
relative to the PP.
p1, p2, p3, p4 = are coefficients of
decentring distortion.
= sym. rad. lens disto. correct.

19. Example
◼ Solution

20. Example
◼ Solution

21. Correction for Atmospheric Refraction
◼ Density or RI of the atmosphere decreases with increasing altitude.
◼ Therefore, light rays do not travel in straight line but bent according to
Snell's law, figure.
◼◼ object point A would be imaged a’.
◼ Angular distor. due refr. is Δɑ.
◼ Refr. cause all im. pts to be diplaced
outward from corc.pos.
◼ Magn. of ref, disto. Increases with
increases of flying height.
◼ Refraction distr. occurs radially from
the photo NP & zero at the NP.
◼ For further read see section 4-12 of the
Element of Photogrammetry by wolf.
◼ Equations do not included for this Lect.