The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
Figure 3: Example for rectification and dense matching. In the upper row the original images are shown, below the rectified pair and 
the computed disparity map. 
one small additional cost P\ is added if small disparity changes, 
e.g. 1 pixel, appear in adjacent pixels of p, whereas the larger cost 
P2 is applied if larger disparity changes are appearing more far 
away. The cost Pi preserves smoothness and due to P2, height 
jumps are forced to appear at adjacent pixels, leading to sharp 
edges in the disparity map. So, for every pixel of interest p of 
the base image, the aggregated costs need to be computed for ev 
ery possible disparity, including the penalties from observing the 
neighbourhood. Finding the final disparity image is equal to the 
task of minimising the energy for the whole image. Such a pro 
cedure would be very inefficient as the complete image must be 
traversed for every disparity. Instead, the problem is formulated 
as a lD-traversing algorithm which sums up the aggregated costs 
at a particular pixel p and disparity recursively and in different 
image directions only. In a last step the disparity for a pixel in 
the base image is selected among all possible disparities as the 
one causing the least summed-up cost. As subpixel accuracy is 
desired, a quadratic curve is fitted through the neighboring dis 
parities and the corresponding costs. The minimum of the curve 
is identified as the optimal disparity value. 
To simplify the matching, the images are rectified beforehand. 
For this purpose the approach proposed in (Oram, 2001) is ap 
plied. In contrast to most other techniques for rectification, this 
approach estimates a non-linear transformation for both images 
with the aim to minimise perspective distortion effects. Besides 
the fundamental matrix, the algorithm uses the original matches 
from the feature tracking to obtain an optimal transformation. In 
order to further stabilise the transformation, additional features, 
like available through SIFT (Lowe, 2004) in the case at hand, are 
incorporated. 
In Figure 3 an exemplary dense matching result is shown. The 
upper row shows the original image from the UAV dataset as de 
scribed in section 3. The lower row shows the rectified image pair 
and the disparity map as resulting from the Semi-Global Match 
ing algorithm. 
2.4 Computation of super resolution images 
In the context of this paper, super resolution images (SRI) refers 
to the process of computing images preserving the same geome 
try as the original images from the sequence, but the colour values 
are computed from the several matches where the image partici 
pated. Actually, in the current implementation, two different SRI 
images are computed: one from the mean value of all correspond 
ing pixel values and one from the median images. As subpixel 
accuracy is derived from the matching algorithm, the target scale 
factor for the SRI can be selected larger than 1. 
2.5 Forward intersection 
A direct solution for the 3D points given observations in multiple 
images is proposed e.g. in (McGlone et al., 2004, Section 11.1.5). 
With an unknown 3D point symbolised by X, the corresponding 
image coordinates in image i by Xi and the respective projection 
matrix by Pi, the constraint 
[xi]xPiX — AiX = Wi = 0 (1) 
is given ([cci] x defines the skew-symmetric matrix of xf). 
All Ai are assembled in a common matrix A. The error w t w 
needs to be minimised, resulting in an optimal point X. This op 
timal point is the right eigenvector of A belonging to its smallest 
eigenvalue, computed through a singular value decomposition.