The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
can be calculated by formula (1). This coherent coefficient is 
the value of the window centre. 
Y= 
(1) 
m n rri ri 
Z Z|w(i,;)| X XI^M 
In the formula, M (i, j), S (i, j) are the plural data of the corresponding 
position (i, j) in two matching windows respectively. The symbol 
represents conjugated plural. The coherent coefficient of every 
point in the search window can be calculated by the formula 
above. The point with the largest coherent coefficient is 
selected as the matching point. 
(2) The greatest spectrum method uses the spectrum value as 
the indicator value. The two matching windows are processed 
by interference processing to obtain the interference fringe 
images. The two-dimensional discrete Fourier Transformation 
(DFT) is processed to the interference fringe images to get the 
two-dimensional spectra. The greatest value of the plural 
absolute value of the two-dimensional spectra is the indicator 
value (spectra value). Finally, the point with the greatest spectra 
value is selected as the matching point. 
(3) The average fluctuation function of the phase difference 
method uses the function value (f) of the phase difference 
average fluctuation as the indicator value. Firstly, the 
corresponding pixel phase differences P (i, j) of the two 
matching windows are calculated, and the function value (f) of 
the phase difference average fluctuation is calculated by 
formula (2). 
/ = 11 (|^0 +1 J) - P(i, j) I +!/»(/, j +1) ■- P(i, y)|) / 2 (2) 
i ] 
Where,f is the indicator value. The point with the least f value is 
selected as the matching point (Lu, 2005). 
2. METHODOLOGIES 
2.1 SIFT algorithm 
2.1.1 Keypoint detection 
The first step of SIFT construction is the detection of a keypoint. 
The main principium: for each octave of scale space, the input 
image is convolved with the Gaussian function to produce the 
set of scale space images. And then adjacent Gaussian images 
are subtracted to produce the difference-of-Gaussian images 
(DoG). Finally, the Gaussian image is Sub-Sampled by a factor 
of 2. A pixel is compared to its 26 neighbors in 3 by 3 regions 
at the current and adjacent scales, detecting the maxima and 
minima of the difference-of-Gaussian images. 
In addition, with the curve fitting method, the keypoint can be 
further processed by precise location. 
2.1.2 The local image descriptor 
Before the local image descriptor, one or more orientations are 
assigned to each keypoint location based on local image 
gradient directions. All future operations are performed on 
image data that has been transformed relative to the assigned 
orientation, scale, and location for each feature, thereby 
providing invariance to these transformations. 
Then, the local image gradients are measured at the selected 
scale in a region around each keypoint. These are transformed 
into a representation that allows for significant levels of local 
shape distortion and change in illumination (Lowe, 2004). 
2.2 Advantages of the SIFT algorithm 
Theoretically speaking, the SIFT algorithm is invariant, even 
for images with scale change and rotation. However, the 
tectonic of SIFT has been specially treated in many details. 
Therefore, SIFT algorithm has a strong adaptation to images 
with complex deformation and changes of light. At the same 
time, it has higher computing speed and higher positioning 
accuracy. 
(1) Compared to the traditional method Laplacian of Gaussian 
(LoG), DoG has higher computing speeds to detect the keypoint 
in scale space. 
(2) The precise position of the keypoint not only improves the 
accuracy, but also improves the stability of the keypoint. 
(3) When constructing the keypoint descriptor, we use statistical 
characteristics on a sub-region level as a research object, not on 
a pixel level, which improves the adaptability to the local 
deformation of images (Zhao, et al., 2007). 
2.3 Coregistration based on sift for insar 
Some commonly used operators for describing characteristics 
are Sum of Squared Difference (SSD), Sum of Absolute 
Difference (SAD), and Normalized Cross Correlation (NCC). 
Directly depending on gray information of images, all these 
operators are sensitive to noise in the images. Thus, the 
robustnesses of these operators are weak during the non-linear 
gray transformation of images. As for a SAR image with mass 
speckle noise, using these operators seems to be unpractical. 
However, the method based on SIFT algorithm shows a 
characteristic of better robustness and anti-interference when 
transforming images in both geometric and optical aspects. On 
the basis of this conclusion, the SIFT operator can be applied to 
the registration of INSAR image processing for getting a better 
result. This result can also be used for further steps of 
interference processing. In this paper, the SIFT algorithm will 
be used in precise matching to improve the accuracy of 
matching and computing speed. The process of coregistration 
based on SIFT algorithm is as follows in Fig. 1. 
Fig.l. the process of coregistration 
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