The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
1289 
In order to exploit the full potential of high-resolution satellite 
images for 3D information extraction it is essential that precise 
georeferencing is applied. Barista handles three different sensor 
models for georeferencing to establish the object space to image 
space transformation and vice-versa. 
3.1 3D affine model 
The 3D affine model is an approximation of the actual imaging 
process by a parallel projection (Fraser and Yamakawa, 2004). 
This approximation is justified by the very narrow fields of 
view of commercial high-resolution satellites. The model does 
not explicitly utilise camera or orientation parameters. The 
transformation relating the 2D image coordinates of a point 
with its object coordinates is given as 
x = aj ■ X + 02 ■ Y + as ■ Z + a 4 
y = a 5 ■ X + a 6 ■ Y + a 7 ■ Z + a 8 (1) 
with X, Y, Z: object coordinates 
x, y: image coordinates 
a,: parameters of 3D affine transformation 
The 3D affine model can be applied independently from the 
type of the object coordinate system; here the adjustments were 
carried out with the GCPs being defined in geocentric, 
geographic, and UTM coordinates. The optimal reference 
coordinate system for the affine model and its assumption of a 
parallel imaging plane is the UTM projection (Fraser and 
Yamakawa, 2004). A minimum of 4 non-coplanar GCPs is 
required to determine the parameters of the 3D affine model. 
3.2 RPC sensor model 
In the case of the RPC sensor model, a set of rational 
polynomial coefficients are used as a camera replacement 
model. They are provided by the image distributors and are 
known to have a significant bias. This bias can be removed with 
at least one well-defined GCP (Fraser et al., 2006). The 
transformation relating the 2D image coordinates of a point 
with its object coordinates is given as 
x + B 0 + 5, • y + B 2 ■ x = 
y + A 0 +A r y + A 2 -x = 
Num x {(p, A, h) 
Den x {(p,A,h) 
Num y (<p,A,h) 
Den y (cp,A,h) 
(2) 
<p, À, h : 
latitude, longitude, and 
ellipsoidal 
height 
x,y: 
image coordinates 
Numx, Deny. 
cubic polynomial functions 
space coordinates for x 
of object 
Numy, Den y \ 
cubic polynomial functions 
space coordinates fory 
of object 
A u Bp. 
affine parameters of bias correction. 
Note that the (altogether 80) coefficients of the four 
polynomials in Equation 2 are distributed by ISRO, so that they 
can be used for direct georeferencing. However, Equation 2 also 
incorporates the bias correction by an affine transformation in 
image space. The parameterisation of the bias correction can be 
changed in Barista. The minimum parameterisation of the bias 
correction is by the two shifts A 0 and B 0 ; if this parameterisation 
is chosen, the other parameters will be set to zero, and they will 
be kept constant in the adjustment. In order to additionally 
compensate for drift effects, the parameters A, and B, can be 
determined. The third option is to determine all the parameters 
A,- and Bj of the 2D affine transformation. The number of GCPs 
required depends on the parameterisation: If only shifts are used 
to model the bias, one well-defined GCP is enough. Two 
appropriately positioned GCPs is the minimum needed for 
determining shift and drift parameters, and three GCPs are 
required for the full affine bias correction model. 
3.3 Generic pushbroom sensor model 
The generic pushbroom sensor model uses a physical camera 
model, modelling the orbit path and attitudes by splines. In 
order to determine the parameters of these splines, direct 
observations taken from orbit path and attitude recordings 
provided by the image distributors are used in the adjustment 
process. Since the definitions of the parameters delivered by 
different data vendors are not identical and sometimes not even 
compatible, the vendor-specific data have to be mapped to the 
model used in Barista when these metadata are imported. Such 
import functions have been implemented for SPOT 5, 
QuickBird and ALOS. The transformation relating the image 
point p/r in the image line coordinate system to the object point 
Vecs in the object coordinate system is given as: 
p F - c F + 5x = A • R M T • {Rp T ^ • Ro T ' [Pecs - StfJ] - C M } (3) 
with P ECS : point in an earth centred system 
S(t): satellite position at time t, modelled by splines 
Ro: time-constant rotation rhatrix, rotating into a 
nearly tangential system 
R P (t): time-dependant rotation matrix depending on 
three rotational angles roll(t), pitch(t), yaw(t), 
each of them modelled by a spline function 
C M : position of the camera centre in the satellite 
(camera mounting) 
R M : rotation matrix from the camera system to the 
satellite (platform) system 
X: scale factor describing the position of the point 
along the image ray 
p F : (xp, 0, 0) T : image coordinates of P in the 
image line (framelet) coordinate system 
c F : (x F0 , yFo, F) T - position of the projection 
centre relative to the image line 
8x: corrections for systematic errors. 
Equation 3 has three components. By dividing the first and the 
second component of the equation by the third, the scale factor 
X is eliminated, and the remaining two equations describe a 
perspective transformation with time-dependant projection 
centre and rotations. The time t is closely related to and can be 
determined from the measured y coordinate of a point, i.e. the 
line index in the digital image; the observedy F coordinate (they 
coordinate in the CCD line) is 0. Both the satellite path S(t) and 
the three angles used to compute R P (t) are modelled by spline 
functions. The orbit path and attitude information provided in 
the metadata files are used as direct observations for 
determining the parameters of the splines. The sensor model 
also contains a model for the correction of systematic errors in