The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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3.2.2 Detection of scale-space extrema 
Maxima and minima of the difference-of-Gaussian images are 
detected by comparing apixel (marked with X) to its 26 
neighbors in 3x3 regions at the current and adjacent scales 
(marked with circles). 
scale 
Figure2: Detection of scale-space extrema 
In order to detect the local maxima and minima of D(x,y,<j), 
each sample point is compared to its eight neighbors in the 
current image and nine neighbors in the scale above and below. 
It is selected only if it is larger than all of these neighbors or 
smaller than all of them. 
3.2.3 keypoint localization 
The scale of the keypoint is used to select the Gaussian 
smoothed image, L, with the closest scale, so that all 
computations are performed in a scale-invariant manner. For 
each image sample, L(x,y) , at this scale, the gradient 
magnitude, m(x, y), and orientation, y), is precomputed 
using pixel differences: 
rr(x,y) =y¡ (Ux+l,y)-Ux-l,y)) 2 +(l(x,y+I)-Ux,y-I)) 2 
6(x,y)=at3^(Ilx,y+I)-Ux,y-l))/(Ilx+l,y)-lJix-l,y))) 
3.2.4 descriptor representation 
Image gradients Keypoint descriptor 
Figure 3 descriptor representation 
A keypoint descriptor is created by first computing the gradient 
magnitude and orientation at each image sample point in a 
region around the keypoint location, as shown on the left. These 
are weighted by a Gaussian window, indicated by the overlaid 
circle. These samples are then accumulated into orientation 
histograms summarizing the contents over 4x4 subregions, as 
shown on the right, with the length of each arrow corresponding 
to the sum of the gradient magnitudes near that direction within 
the region. This figure shows a 2x2 descriptor array computed 
from an 8x8 set of samples, whereas the experiments in this 
paper use 4x4 descriptors computed from a 16x16 sample array. 
When SIFT eigenvectors of two images are generated, we will 
use Euclidean distance of eigenvectors of key points to measure 
similarity of key points in two images. Get certain key point in 
image 1, and find in image2 two key points that are nearest in 
Euclidean distance. Among these two points, if quotient of the 
nearest distance divided by sub-nearest distance is less than 
given threshold, then these two matching points are accepted. 
Decreasing the threshold will decrease the SIFT matching 
points but will be more robust. 
3.2.5 Improvement of control error matching in SAR 
image. 
When matching keypoints, in a cluttered image, many features 
from the background will not have any correct match in the 
database, giving rise to many false matches in addition to the 
correct ones. The correct matches can be filtered from the full 
set of matches by identifying subsets of keypoints that agree on 
the object and its location, scale, and orientation in the new 
image. The probability that several features will agree on these 
parameters by chance is much lower than the probability that 
any individual feature match will be in error. 
In this paper, the method of removing false matching points is: 
(1) Rough location is completed with the support of SAR images 
POS data. We can locate one SAR image to reference SAR 
image approximately with POS data. When the distinction 
location of key points pairs more than the rough location locate 
by POS, the key points will be removed. 
(2) Correlation coefficient control wrong match. Correlation 
coefficient, is the standardization of covariance function, equal 
to Covariance function divided by the variance of two signals. 
The correlation of g(x,y)znd g (jc ,y ) is: 
p(p,q) 
c{p,q) 
Vc.c./o’,,) 
The first thing In dealing with SAR images is to determined 
threshold. . We excavate an certain size of window both in 
the neighbours of keypoints a ‘ in target image, and the 
neighbours of keypoints ' in the reference image, extracted by 
SIFT. For example, we excavate two windows with key points 
centered, of which size is 50 x 50, and compute the correlation 
coefficients ^*', store the values and shift to next key point 
^ 1+1 of real-time image. After computing all the coefficients of 
key point centered windows in real-time image, rank all the 
coefficients ••• ( where n is the number of 
matching points that detected by SIFT) from maximum to 
minimum and set the threshold 
Po=(Pma X -Pmin) Xk + Pmi„