ISPRS Commission III, Vol.34, Part 3A »Photogrammetric Computer Vision“, Graz, 2002 
  
2. A GLOBAL OPTIMAL IMAGE REGISTRATION 
Suppose /, and /, are two images to be registered and they 
are acquired from the same geographical area on different dates 
or with different sensors. Here, /, is defined as a reference 
image, and /, to match the reference image is defined as a 
sensed image. The goal of the image registration is to rectify 
the sensed image 7, into the coordinate system of the reference 
image /, and to make corresponding coordinate points in the 
two images correspond to the same geographical location. We 
assume that a geometrical transformation between the two 
image coordinate systems can be expressed by a unity 
polynomial mapping function, i.e.: 
Bk 
E 3^ —m o 
x-Pü (rz) > Y 8 (1) J» 
k=0 m= E nm (1) 
Rk 
xt [s m 
=F, (x yı)= > 2, Pen) A2. Va 
Met) 
k=0 m= 
Where Re{l2} represents a order of the polynomial, 
Cefn (0212 ED) is a set of the polynomial 
coefficients. Apparently there are six and twelve unknown 
parameters in the set C, and C, respectively. Thus, the central 
issue of the image registration is now to acquire the optimal 
coefficients Cy - 
In the existing methods, control points are used to approximate 
coefficients C, by the least-squares method. However, their 
fitting results are not the global optimal because only several 
limited local control points are employed to estimate 
coefficients c,. Therefore, a new method must be developed to 
compute the optimal coefficients C, . . 
The global optimal coefficients C, are the coefficients 
determining a geometric transformation through which the 
sensed image 7, is completely matched with the reference 
image /,. If measures for evaluating the match between two 
images are regarded as an energy function, the optimal 
coefficients c, can be estimated through the energy function 
optimization, i.e. 
Cr, = arg max(Energy(C A )) (2) 
In the following, we firstly discuss how to define the energy 
function, and then address the detail of the optimization. 
2.1 Definition of the energy function 
For two images taken at difference dates with the same 
sensor, there may be radiometric distortion due to variations in 
solar illumination, atmosphere scattering and atmosphere 
absorption, but structural features in the two images are 
basically consistent. These structural features include straight 
lines, closed curves, contours, regions, and so on. Even for two 
images acquired from difference sensors, structural features 
might have changed in the local range, but many salient 
structural features seldom change, such as roads and flat areas. 
Structural features are usually grouped by many edge points, so 
if there are no changes in the structural features, it is reasonable 
to assume there are no changes in the distribution of edge 
points. In other words, an edge point is likely to exist in the 
reference image /, at the location where there is an edge point 
in the sensed image 7, , and vice versa. Usually, all edge points 
are the local maximal of magnitude, thus their average edge 
strength is also the maximum. Therefore, an average edge 
strength of points in the reference image 7, that are converted 
from edge points in the sensed image /, by using geometric 
transformation determined by the global optimal coefficients 
C, Should be the maximum. According to this assumption, 
we can define the average edge strength as the energy function. 
Let Æ, = (x, », Jsis N)j the edge points extracted from the 
sensed image /,, where N is the number of edge points, and 
let image M, represent the edge strength (or magnitude) map 
of the reference image /, . The energy function is defined as: 
Energy(C FÈME t. (x, Va )F E (s, vs, ) (3) 
where E ix. j »,) and F, (x,,y,) are computed in equation (1), 
x Yr 
M, (x,y) represents the edge strength of point (x, y) and needs 
bilinear interpolation because F, n and F, (x,,y,) are 
real. 
2.2 The energy function optimization 
The energy function Energy(C,) in equation (3) is a non-linear 
high dimensional function, and has many local optima. 
Determinative local search methods are easily entrapped in a 
local optimum. By contrast, random global search algorithms 
are less likely to be trapped in local optima, but their . 
computational costs are much higher. Therefore, not any one 
method solves this problem very well and the tradeoff is to 
combine them [5]. In this paper, we combine a random search 
algorithm and a determinative search method into a hybrid 
approach. In calculation, the approach is composed of the 
following two steps: firstly, we look for many sets of initial 
guesses of coefficients C, in the global range by using a 
random search algorithm, and then we acquire the optimal 
coefficients C, near these initial guesses by a determinative 
search method. 
Considering that it is not easy to gain the gradient of the energy 
function Energy(C x) , we choose a SM [6] as the 
determinative search approach and GAs [7] as the random 
search algorithm. The whole optimization procedure is 
implemented in three stages: in the first stage, use the manual 
method to determine the initial guesses and the range of each 
parameter in coefficients C, . In the second stage, for each 
parameter, acquire initial guesses closer to the optima with 
GAs. In the last stage, exploit a SM to search the best 
coefficients C, . The detail of each method is given in the 
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