The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B3. Beijing 2008 
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N j=Yj c i^ ( 13 ) 
R 1 
4) To compare all values of N and get the maximum of them, 
N k =max{N ] N 2 ---Nj} (14) 
Thus k corresponding to the coordinate of (r k ) in the image is 
the comer point. 
Figure 3 shows one example of comer point recognition. The 
method depends on binary image morphology after feature 
extraction, instead of recognizing the comer points on 
gray-scale images. Thus it can locate the comers accurately 
without gray and geometry threshold. 
(a) Edge feature image (b) Comer recognition result 
Figure 3. Comer points’ extraction 
4. IMAGE MATCHING BASED ON LIFTING ASWLET 
4.1 Anti-symmetric lifting wavelet and the decomposition 
and reconstruction of image 
In this section, a novel “split-merge-split” lifting algorithm for 
anti-symmetrical wavelet is proposed and can be realized 
through the following steps: 
1) Supposing f[x, y) is the image function, first let the image 
split at the horizontal direction. The result is to deposit the low 
frequency information of image s c at even number positions, 
and deposit the high frequency information dc at odd number 
positions, as follows (Lin, 2007), 
Split(fj) c =(s c ,d c ) (15) 
*C=HJj 
d e = GJj 
(16) 
2) After finishing splitting and decomposing in every row, 
do the merge once more. Then get the horizontal direction 
decomposed image. 
(fj)r = mer ge(s r ,d r ) (17) 
3) To split the image at the vertical direction (the serial 
number of image row is r). The result is to deposit the low 
frequency information of image ss at even number position at 
horizontal and vertical directions, and deposit the high 
frequency information sd,ds,dd at the crossed position of even 
and odd numbers , as follows, 
(ss,sd ^ 
(18) 
(ss.sd 
(18) 
ss = HXfj) c 
c, r are even number 
sd = H r {f j ) c 
ds = G r {fj) c 
c is odd number, r is even number 
c is even number, r is odd number 
• (19) 
dd - G r (fj ) c 
c, r are even number 
4) Taking the low frequency image ss as a new input, 
proceeding the next level decomposition, and if it meets the 
demand we can stop the decomposition. 
Figure 4 represents the four steps described above. 
According to the decomposition method, the formed image 
presented parity permutation. Figure 4 shows the 
decomposition algorithm of ASWlet lifting wavelet, when 55 is 
the low frequency information; sd is the vertical direction 
feature; ds is the horizontal direction feature; dd is the diagonal 
direction feature. During the operation we did the (2j-l) of 
interval extraction. 
The method could maintain the on-site computation property of 
lift wavelet. In the meantime, it has a strong expressive ability 
as for the high frequency feature of the three constituent 
(vertical, horizontal and diagonal direction) on the decomposed 
image. The result of wavelet transform could be used in image 
match. 
Imaged reconstruction can be realized according to the inverse 
process of the above-mentioned steps. Figure 5 shows the 
results of image decomposition by using ASWlet lifting 
wavelet and the linear lifting wavelet. 
Figure 4. Decomposition algorithm ASWlet