In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
1.2.1 In-situ calibration: The in-situ methods of calibration 
are purported to produce the best camera calibration results. 
They are mostly used for calibrating large cameras that cannot 
be easily calibrated in laboratories. The cameras are hence 
calibrated while they are in operation. In-situ calibration 
methods require an area (a calibration range) with a very dense 
distribution of highly accurate control points. While 
maintaining a high density, the control points in the calibration 
range should be well distributed in the horizontal, as well as in 
the vertical direction. A rigorous least squares block adjustment 
based on the co-linearity equations, augmented by equations 
modelling radial and decentring distortion (Eq. 5) can generate 
accurate calibration parameters. The in-situ method requires 
aerial imagery over a calibration range. Also, careful 
maintenance of the calibration range is required, over the years. 
The maintenance may include re-survey of the control points, 
making sure they are undisturbed etc. All these factors can be 
expensive and time consuming for the camera operators. 
1.2.2 Precision multi-collimator instruments: The USGS 
operates a multi-collimator calibration instrument located at 
Reston, Virginia, USA (Light, 1992). The instrument is used to 
calibrate film based cameras, and while digital cameras are 
increasingly used, there are a number of photogrammetric 
companies that still employ film cameras. The aerial camera is 
placed on top of the collimator bank, aligned and focused at 
infinity. Images that capture the precision targets located in 
telescopes lens (of the multi-collimator) are taken. The 
deviation of the measured image (x,y) coordinates from the 
known (X,Y) coordinates forms the basis for solving for the 
calibration parameters (Eq. 5). 
1.2.3 Self calibration: Self calibration uses the information 
present in images taken from an un-calibrated camera to 
determine its calibration parameters (Fraser, 1997; Fraser 2001; 
Remendino and Fraser, 2006; Strum, 1998). Methods of self 
calibration include generating Kruppa equations (Faugeras et. 
al., 1992), enforcing linear constraints on calibration matrix 
(Hartley, 1994), a method that determines the absolute quadric, 
which is the image of the cone at a plane at infinity (Triggs. 
While there are many techniques employed by researchers 
(Hartley, 1994; Faugeras et al., 1992), most of these do not find 
solutions for distortion and principal point, as they are not 
considered critical for Computer Vision. On the other hand, for 
photogrammetrists, these are critical parameters necessary to 
produce an accurate product at a reasonable price. 
In this study, we will use self calibration techniques to 
determine camera calibration parameters. Section 2 provides a 
brief theoretical framework for calibration. It goes on to discuss 
the design of two methods for self calibration used at the USGS, 
and describes the experimental set-up. It introduces an 
inexpensive method for calibrating small and medium format 
digital cameras, with short focal length. Section 3 analyses the 
results of calibration, and compares the results obtained from 
the two methods described in Section 2. Section 4 presents the 
conclusions and discusses future work. 
2. CALIBRATION METHODOLOGY 
2.1 Theoretical basis 
The self calibration procedure described in this research is 
based on the least squares solution to the photogrammetric 
resection problem. The well known projective collinearity 
equations form the basis for the mathematical model. 
x- 
m ii(X-X c ) + m 12 (Y- Y c ) + m 13 (Z-Z c ) 
m 3l( x ~ X c) + m 32( Y ~Y c ) + m 3 3(Z-Z c ) 
0) 
y-y P 
f m 2 ,(X-X c )+m 22 (Y-Y c ) + m 23 (Z-Z c ) 
(_ m 31 (X - X c ) + m 32 (Y - Y c ) + m 33 (Z - Z c ) 
In Eq. 1, (x ,y) are the measured image coordinates of a feature 
and (x p , y p ) are the location of the principle point of the lens, 
in the image coordinate system, f refers to the focal length and 
m ,i m 12 m 13 ' 
m 21 m 22 m 23 
is the camera orientation matrix. Since the lens 
V m 31 m 32 m 33, 
in the camera is a complex system consisting of a series of 
lenses, the path of light is not always rectilinear. The result is 
that a straight line in object space is not imaged as one in the 
image. The effect is termed distortion. Primarily, we are 
interested in characterizing the radial distortion and de-centring 
distortion. Radial distortion displaces the image points along 
the radial direction from the principal point (Mugnier et al., 
2004). The distortion is also symmetric around the principal 
point. The distortion is defined by a polynomial (Brown, 1966; 
Light, 1992). 
5r = kjr 3 + k 2 r 5 + k 3 r 7 +... 
r = ^( x “ x P ) 2 +(y-y P ) 2 
kj,i = 1,2,3...aœ coefficien ts of the polynomial 
The (x,y) components of the radial distortion are given by: 
8Xj 
s Yi 
(3) 
The second type of distortion is the decentring distortion. This 
is due to the displacement of the principle point from the centre 
of the lens system. The distortion has both radial and tangential 
components, and is asymmetric with respect to the principal 
point (Mugnier et al., 2004). The components of de-centring 
distortion, in the x-y direction are given by