The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
2. IMAGE-SEQUENCE REGISTRATION 
Movement of the camera results in recording different images. 
In principle, reconstructing an image in the new camera 
position is possible from the previous image by knowing the 
movement of the camera and the distance of an object in the 
scene to the camera. 
Using wrong transformation parameters between two images, 
results in a transformed image that is not oriented in the same 
way as the reference image. The first image is the reference 
image and the second one the candidate image which should be 
registered to the reference one. The mismatch can be visualized 
by differences between the reference image and the transformed 
candidate image. The Mean Square Error (MSE), is used to 
express the misalignment between the transformed image and 
the reference one. The optimized transformation parameters are 
those that provide the maximum agreement between the 
reference and transformed candidate image. 
Consequently, the transformation parameters are the ones where 
the difference between the transformed image and the reference 
image is minimal. In other words, the transformation parameters 
are obtained by minimization of the MSE between the 
transformed image and the reference image. 
2.1 Transformation Parameters 
In this paper a projective model without shearing and different 
scale parameters is used as a transformation model on the 
calibrated images (Heikkila, 1997; Zhang, 1999). This model 
can be described by: 
Searching the whole parameter space for finding the optimum 
value is computationally very expensive. The complexity is 
°<n", ) with n pi the number of all possible values for each 
parameter, p h and no the number of parameters. In our case the 
search space is 6-dimensional. One could imagine the real 
number, M , as the search range for each parameter. However, 
not every combination of parameters is allowed. Each 
parameter has a certain range beyond which the transformed 
image is meaningless. Moreover, for each parameter there is a 
resolution value such that within the resolution value the 
transformed images are equal. Although incorporating range 
and resolution of parameters reduces the search space, still the 
number of potential parameters is quite high. 
2.2 Differential Evolution 
Therefore, we have applied a global optimization technique. 
Here Differential Evolution (DE) (Price et al., 2005) is used to 
find the global optimum. 
DE starts with an initial population of q randomly (McKay et al. 
1979) chosen parameter value combinations m. These m’s are 
improved during successive generations of constant size q, in 
the sense that a descendant replaces an m, becoming its 
successor, if it has a lower energy value. The distinctive feature 
of DE is the way in which these descendants are created. 
Various ways to generate new m’s exist, but here only the 
following procedure is considered. At the start of generation k 
the parameter vectors m kl ,...,m k-q are given and for each of 
them a descendant is created. To create a descendant d k>j a 
partner p k-i is constructed as follows: 
X, = 
F, = 
scos(û)x 2 + ssin(0)y 2 +t ] 
v l x 2 +v 2 y 2 +\ 
-ssin^jx, + s cos(0)y 2 +t 2 
) = 111 
k,i k,j t 
+ F(m 
, -m, ) 
k J 2 k ’h ' 
(3) 
(1) 
V ,^2 + V 2-V 2 + 1 
S, 0, tj, t 2 , v/, and v 2 are respectively scale, rotation, 
translational and special projective parameters, xj and y I are 
image coordinates of the first image and x 2 and y 2 are the image 
coordinates for the second image. All the image coordinates are 
given w.r.t. the center of the image at hand. As a consequence 
our parameter space is six dimensional. Each point in parameter 
space is a parameters’ combination which corresponds to a 
transformed image and therefore to an energy value. 
The Mean Square Error (MSE) is used as an energy function: 
with the three different m-vectors chosen at random from the 
population and F a scalar multiplication factor between 0 and 1. 
The descendant d ki j of m k j results from applying crossover to 
m ki and p k q with crossover probability pc. A higher value of pc 
leads (on average) to more dimensions of p k-i being copied into 
m k>i . Descendant d k i only replaces m ki , becoming its successor, 
if its energy is lower. The setting parameters of DE are 
population size q, multiplication factor F, crossover probability 
pc and the number of generations NG. The values chosen for 
the setting parameters are used according to (Snellen and 
Simons, 2007). 
Two types of image registration occur in our data sets: 
registration between consecutive images and registration 
between an arbitrary image to the reference image. There is a 
high correlation between image frames because of the 
helicopter hovering to keep the viewing area fixed. However, 
shaking of the helicopter causes a drift. This movement can be 
enhanced by increasing temporal differences. The small 
movement between consecutive frames and the high correlation 
between image frames direct us to the design a framework for 
the registration of two arbitrary images to avoid excessive 
computations. A final result of this framework, after applying it 
to all available frames is a stabilized image sequence. The 
framework is summarized as follows: 
1. compute Tj+ij, the transformation between I i+! and /, 
2. compute T j+n = 7^7} the estimated transformation 
between Im and 11