In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds), IAPRS. Vol. XXXVIII. Part 3A - Saint-Mandé, France. September 1-3. 2010 
domain. RPCs define the rational polynomial functions that 
map a real world coordinate to the image domain. Therefore, 
once we have the RPC coefficients, we have the projection 
functions. Thus, for each point in the SRTM data, we can find 
its projection pixel in the image. 
It is known that SRTM accuracy is unchanged when 90m 
resolution SRTM data are upsampled by 3 to obtain 30m 
resolution, via bi-cubic interpolation [Keeratikasikorn 2008]. 
Therefore, in this study, the SRTM data are upsampled by 3 
with bi-cubic interpolation and registration is performed for the 
upsampled version. 
Once the SRTM points are projected onto the image, an 
interpolation is required to fill the empty pixels. The SRTM 
data is regularly-sampled (30m or 90m Ground Sample 
Distance; GSD). On the other hand, satellite images have higher 
resolution and do not sample the Earth surface on a regular 
latitude-longitude grid. 1 degree x 1 degree SRTM patches and 
satellite images are never aligned. In other words, the SRTM 
grid does not project to another regular grid in the image 
domain and some SRTM points will fall outside the image, 
especially for narrow FOV satellite images, such as IKONOS. 
Thus, an interpolation scheme is required that provides 
acceptable accuracy, and leaves no empty pixels. 
For that purpose, quadratic polynomial surface fitting is applied 
as follows: For each SRTM point p s , eight neighbours of that 
SRTM point are projected to the image domain to define a 
surface patch sampled at 9 points, together with the centre point 
p s (Figure 1). Then the projection points are taken as examples 
from quadratic polynomials (on image coordinates) that define a 
height function, a latitude function and a longitude function; 
Fj = a,.vr + bj.v 2 + Cj.u.v + d,.u + e,.v + f (1) 
where 
u, v = image row and column indexes 
i = 1,2,3 for height, latitude and longitude. 
a„ b it Cj, d h e„ f - coefficients of the polynomial 
overlapping region take the average of the values assigned to 
them by different patch polynomials 
2.2.Elimination of Bias in SRTM-Image Registration 
The bias in RPC is mainly due to errors in satellite's position 
and look direction. The latitude and longitude of the satellite, as 
well as the look direction, are measured with some error. 
Although these errors affect directly the inputs of the RPCs 
(erroneous latitude and longitude), bias correction is usually 
achieved in the image domain with correction terms for both 
image coordinates u and v. 
Considering the above-mentioned reasons for projection bias, 
performing the correction in the object domain may be expected 
to provide better results. Still, in this study both image and 
object domain correction are tested. 
From the previous experiments in the literature, it is known that 
the RPC bias is around 5 meters and not larger than 10m (for 
high resolution satellites, such as IKONOS) [Dial 2002a, 
2002b]. Additionally, coarse SRTM error figures are available 
for the entire SRTM coverage [Rodriguez 2005]. Thus, one can 
determine a search region boundary for bias elimination terms. 
For bias correction, the following search scheme is adopted: 
i. Both images are registered with the method described in 
2.1. 
ii. A modified optical flow estimation method (Kanade- 
Lucas Tracker (KLT) [Bouguet 2000] with varying 
pyramids and backward consistency) is used to 
determine a few number of reliable stereo 
correspondences (tie points) (Although KLT is not 
common for correspondence estimation applications, 
with proper modifications, KLT could provide 
impressive results with many image correspondences 
with relatively small computational complexity). 
iii. Quantized brute-force search is performed in the search 
region as follows: 
In other words, interpolation functions are defined separately 
for latitude, longitude and height. 
(a) (b) 
Figure 1. (a) The nine-point SRTM grid and (b) their 
projections on the satellite image. 
The 6 polynomial coefficients are solved by using 9 equations. 
The empty pixels that lie in the neighbourhood of the centre 
pixels (blue region in Figure 1) are filled by using the 
polynomial. Overlapping of the neighbourhoods is forced to 
avoid empty image pixels. The values of pixels that lie in the 
Let pi = (u,, v/), p 2 = (uvj) be any correspondence between 
images L and I 2 , and Pi = (lafi, loni) , P 2 = (lat 2 , lon 2 ) be their 
initial registration vectors (determined by the method described 
in Section 2.1). The following algorithm is proposed for 
determining the candidate correction vectors: 
For each correction vector AP = (Ai at , Au»), 
error = 0 
For each stereo correspondence pair (p t , p 2 ) 
Take single-image registration value Pi for p t 
P', = P, +AP 
p’ 2 = Project( P'i) onto I 2 
error = error + || P: -p ’i || 2 
end correspondences 
end correction vectors 
Next, the correction vector with minimum error score is taken 
as the bias correction vector. 
Since the bias has a strong DC term for the entire image, this 
search is performed only once with a few “good” tie points.