International Archives of the Photogrammetry, Remote Sensing 
and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
is usually quite good, contemporary cameras often give 16 bit 
data with twelve bit information. 
There are also disadvantages for such cameras: Usually they are 
much more expensive than standard digital CCD video cameras. 
If we take diffraction at the aperture as limit for the angular 
resolution a lens for a thermal camera may have to be ten times 
bigger than the equivalent lens for the visual camera. Also often 
the detector has to be cooled down to very low temperatures. 
Therefore thermal cameras are usually bigger and need more 
energy than visual cameras. They also do not give any spectral 
measurements like a colour CCD camera does. Some modern 
thermal cameras have a focal plane array sensor but some 
systems still have only a small number of sensors. These 
cameras compose the image using moving mirror systems, 
which gives special distortions in the image geometry. 
Because of the lack of colour and because of frequent 
appearance of non-structured homogenous regions with no 
temperature differences thermal videos pose a more difficult 
challenge to geometric estimation procedures. Therefore all our 
examples are picked from this domain. The algorithms also 
work for aerial videos of the visual spectral domain with colour 
being an important feature for correspondence assessment. 
2. ESTIMATING POSE FROM HOMOGRAPHIES 
2.1 Interest Point Locations 
It is not possible to localize correspondence between different 
frames if the object is homogenous in that location. If an edge 
or line structure is present at a location in the 2-d image array 
there may still be an aperture problem. Secure point 
correspondence can only be obtained at locations where a 
corner, crossing or spot is present. It is proposed to use the 
averaged tensor product of the gradient of the grey-values 
(Fórstner, 1994). Interest locations are given where both eigen- 
values of this matrix are non-zero. 
2.2 Assessment of Correspondence 
Correspondence between locations in different frames of a 
video can be assessed using grey value correlation. Still there 
may be problems with repetitive structures. However, there will 
usually be a prior estimate for a location correspondence. Then 
this might be used to assign regions of interest in one image to 
interest locations in the other image or to form the overall 
assessment as product of correlation and prior probability. 
Regions of interest or the variance of priors will be quite narrow 
for immediately successive frames of the video. 
2.3 Planar Homographies 
Given a perspective projection and a rigid planar scene the 
movement of locations in the image is determined by a planar 
homography x zx, where the image location correspondence 
(xx ') is written in homogenous coordinates, H is a 3x3-matrix 
and = means equality up to an unknown scale factor. Given a 
set of at least four correspondences H can be estimated using 
direct linear transformation (DLT) (Hartley; Zisserman, 2000). 
We assume the inner camera parameters to be known and the 2- 
d coordinates to be normalized such that the focal length equals 
one and the origin is at the principal point. Shifting the principal 
point has no major impact on the precision of the estimations. 
But the influence of the focal len 
oth is considerable: Either we 
may do the estimation first and 
transform to normalized 
coordinates afterwards using 
fo Wt hs : hy, h, M fh. ) (1) 
hy, hy A|[—| ^ ^» V/ ha 
E. fa My fh dh. hi ) 
Then we will enlarge errors on the projective elements h;, and 
lh; respectively by factor f and diminish errors on the 
translation elements 4,3 and 4,3 with the same factor. 
Or we may do the transform on the image coordinates x and x' 
dividing the first two components of them through / and go into 
the DLT system with these smaller entries. This has a similar 
effect: The equation system will not be balanced. Entrances 
responsible for unknown variables hy; h;> h>; hz2 in the affine 
section will be smaller than the entries for the unknown 
translation elements /jj5 and /;; with approximately the same 
factor / and for the unknown projective elements /15; and A132 
respectively there will be very small entrances (factor f°). 
2.4 Decomposition of Homographies 
Given an estimate for the normalized planar homography H we 
can reconstruct the pose parameters using the decomposition 
HH = Rn), (2) 
where R is an orthogonal rotation matrix, / is the translation of 
the camera and # is the surface normal (Faugeras, 1995). This 
representation sets the origin of the 3-d system into the centre 
of the second camera. R contains three degrees of freedom that 
may be extracted as successive rotation angles or as normalized 
axis in 3-d and turning angle around it. The vectors 7 and ¢ 
together contain five degrees of freedom because n will be 
normalized setting the distance of the second camera to the 
plane to one, while / is a 3-d translation. 
The absolute scale cannot be determined from the image 
sequence alone. This requires additional information e.g. from 
an altimeter or from a speed sensor. 
In rural areas the plane will be a good approximation for the 
ground plane. In urban areas most visible structure will result 
from the roofs. So the plane will be at average roof height over 
ground. The vector 7 will still be a good approximation to 
zenith direction. We will not get information on the north- 
direction from the images unless we rely on shadow and 
daytime analysis. There will be no geo-reference from the 
images as long as we have not recognized or matched objects 
from the images to map objects. 
We assume sufficient movement of the air-craft. This is 
important, because the decomposition of homographies needs to 
distinguish the translation-free case from mappings with 
translated cameras. 
The rotation free case: Often the camera will be mounted on a 
stabilized platform or the camera rotation will be measured by 
an inertial device giving much more precision than the 
estimation from the camera May yield. This known rotation 
may be applied as homography to the coordinates of the first 
image and then we may assume R to be the identity. Then the 
homography is restricted to be à central collineation with real 
eigenvalues, which is either a planar homology or elation 
( Beutelsbacher; Rosenbaum, 1998). Considering the homology 
case first we may scale H such that the double eigenvalue 
equals one. The corresponding 2-d eigenspace is the horizon 
line. This is a straight line of fixed-points (the image of the 
intersection of the plane n with the plane at infinity) and n also 
gives its Hessian normal form. The other eigenspace is 1-d and 
gives the epipole and translation rt. The eigenvalue 
c 
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