PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2015
689
2) Empirical Correction Model:
At times, users are less
interested in the strict physical self-calibration of the
camera and more interested in a general model that can
reduce or eliminate the effect of the systematic errors
within the imaging system, which were left uncorrected
by conventional calibration or by different correction
models applied to the data at different stages of the
mapping process. In this case, rather than employing a
self-calibration with a “Physical AP Model,” additional
parameters in the form of a high power polynomial
function of the image x,y coordinates, are used to model the
systematic error in the image space. Different additional
parameters were used over the years, some of which you
mentioned, the well-known 12 parameters and the 44
parameters correction models. Equations 1 and 2 show
the 12 parameters empirical model developed by Professor
Heinrich Ebner in 1976.
= 1 + 2 3
(
2
2
4
2
3
)
+ 4 + 5
(
2
2
2
3
)
+ 7
(
2
2
2
3
)
+ 9
(
2
2
2
3
)
+
11(
2 2
2
3
)(
2 2
2
3
)
…………………………………………………………………………………………………. (1)
y= 1 + 2 + 3
4
(
2
2
+ 4
2
3
)
+ 6
(
2
2
2
3
)
+ 8
(
2
2
2
3
)
+ 10
(
2
2
2
3
)
+
12(
2 2
2
3
)(
2 2
2
3
)
……………………..………………………………………………. (2)
Where,
∆x, ∆x ………………… Corrections applied to the x and y
image coordinates, respectively;
B ………………………. Airbase at photo scale;
b
1
through b
12
…… The 12 additional parameters.
Empirical self-calibration is popular for mapping processes,
where the model setup is based on densified ground control
and not on the exterior orientation parameters such as
stereo compilation on analogue or semi-analytical plotters.
However, because the polynomial fitting is very powerful in
modeling many of the distortions surrounding the operational
environment of today’s digital and film cameras, it is also
effective in other practices and applications of photogrammetric
mapping.
We need to be careful about the use of the term “self-
calibration” and its departure from the definitions provided
by the “Manual of Photogrammetry.” Unfortunately, most of
the time software companies use the term “self-calibration” to
refer to the empirical AP model. I advise users to adhere to
the industry standard when defining scientific and technical
terms.
In summary, all cameras, including the large format metric
digital cameras, inherit systematic errors due to film or CCD
deformation and other physical characteristics that cause
deviation from perfect satisfaction of the collinearity condition
(when the line connecting the point on the ground, its image
location, and the lens perspective center is not straight).
Imperfection in modeling the earth curvature, the atmospheric
refraction, lens distortion, electronics signal synchronization,
GPS signal synchronizationare additional sources of systematic
errors in the photogrammetric model beside the film/CCD
deformation. Uncorrected systematic errors can have adverse
effects on the mathematical model during aerial triangulation.
This leads to a compromised vertical and horizontal accuracy
of the final products. Years ago, during the analogue approach,
when the software, if any, did not have modeling capabilities,
a grid plate was used during compilation or on the film within
the camera to model distortions due to film deformation and
possible lens distortion. Traditionally, cameras are calibrated,
including lens distortionmodeling, in a laboratory environment
and some residual systematic errors remain uncorrected due
“Imperfection in modeling the
earth curvature, the atmospheric
refraction, lens distortion, electronics
signal synchronization, GPS signal
synchronization are additional
sources of systematic errors in the
photogrammetric model beside the
film/CCD deformation. Uncorrected
systematic errors can have adverse
effects on the mathematical model
during aerial triangulation”
“At times, users are less interested in
the strict physical self-calibration of the
camera and more interested in a general
model that can reduce or eliminate the
effect of the systematic errors within the
imaging system”
