International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
3.IMAGE MATCH AND SPATIAL FEATURE 
POINTS CORRESPONDING 
3.1 Object feature point extraction 
Acquiring the feature points from the picture is the first step of 
matching. The present study applied the Harris operator that is 
commonly used in the computer vision community. Harris 
operator has the following features: it is simple, stable, and 
insensitive to the noise and illumination, it can quantitively 
extract feature points, and the distribution of obtained feature 
point is reasonable. The expression of Harris operator is as 
below: 
M - Gs) el G) 
e Ed 
S.S, S, 
I « Det(M)- kTrace? (M),k = 0.04 
where g and g indicate the x and y directional derivatives 
respectively; G (s) is Gauss template, C9 is convolution 
operation; 4 is interest value of each point; Det is matrix 
determinant; À is constant. 
3.2 Initial matching 
The goal of initial matching is to determine a candidate match 
concourse T. Correlation score was used here. For each feature 
point M, € imagel, M, € image2, Supposes their image 
coordinates are (u, Vi) > (i, v,) respectively, if the 
difference between coordinates m, and m; is less that a certain 
threshold, the grayscale 
(2n+1)x(2n+1) window centered in m, and m, was 
calculated individually. 
Score(m, ; m,) = 
n m 
S ln, *hW € j)- FQ v ]*lr Gr, * f 9. 3)- £u. v.) 
(2n+1)(2m +1) Jo} (I, )x (1) 
where (4) 
pw j- 
S$ fir vr ine Tm + 11] 
i=-n j=—m 
is the average at point (24, V) of f; (k =1,2),and o(I, ) is 
the standard deviation of the image, / y in the neighbourhood 
(2n +1) x (2m + 1) of (, V) which is given by 
  
  
m 
Y Y sv) 
EYES Ÿ 
| 2 (2n 4 D)(2m 4 I) ; e D 
The score ranges from —1,for two correlation windows, which 
CE 9^ 
are not similar at all, to 1,for two correlation windows, which 
are identical. 
A constraint on the correlation score is then applied in order to 
select the most consistent matches: For a given couple of points 
to be considered as a candidate match, the correlation score 
must be higher then a given threshold. If the above constraint is 
fulfilled, we say that the pair of points considered is self 
consistent and forms a candidate match. For each point in the 
first image, we thus have a set of candidate matches from the 
correlation score of 
720 
second image (the set is possibly nil); and in the same time we 
have also a set of candidate matches from the first image for 
each point in the second image. 
Assigns a pair matched point, if it is thought as the candidate 
matched point, the correlation score must be bigger than some 
threshold value. (threshold value is 0.8 in this paper). The size 
of search window is usually determined by priori knowledge 
(the size of corrlated window is 11x11 in experiment). 
Therefore, the candidate match relations between a certain 
feature point in image ! and some feature points in image 2 is 
established. This point was then joined to the candidate match 
concourse T. 
3.3 The relaxation law that is based on matching support 
The law of relaxation is to allow the candidate match pair in T 
to dismiss oneself and to automatically match each other 
through iterative so as to make the “continuity” and 
"uniqueness" to obtain biggest satisfaction. The continuity 
refers to the massive other corret match pair usually existing in 
the neighborhood of correct match pair; Uniqueness refers to 
the identical feature point existing in only one matched pair. Or 
it can be expreesed as the phenomenon that if candidate 
matching is right, there must be many candidate matching 
around it, while if candidate matching is wrong, there are less 
candidate matching around it. Matching support is defined as 
the degree that the neighbor candidate supports the candidate 
matching. It means that the strongest the matching support is, 
the more possible that the candidate matching is true. 
The detailed calculation is as below: 
Supposes there are two set of feature points 
P=tR, p, TERT B. ) and Q- Q, ; Q, jh Q, }.For each 
paired point (P ; Q ; ), relative excursion between two set of 
feature points is defined. Given 0, (hk) is the distance 
between p and Q, when P, and 0 j matches (only shift), If 
10; (h,k) | is zero, it means that Q, corresponding Q, equals 
to gp corresponding P , therefore, points pair ( P ; Q, ) 
should give ( P, j Q; ) strongest support. Along with 
lo, (h,k) | increasing its support decreases. As a result, given 
the support of ( PB, ; Q, )on( p ; Q ) is: 
] 
ó. (A, k) ) 2 ————— (5) 
$( 0; (, k)]) TERY: 
It is reasonable require when (P j Q j Jis a good match, B 
match with Q, only, that is (P, ; Q, ) is related with p and 
be paired to( p ; Q j )with maximize support. a measure of 
support for a match is defined below: 
max (16, (h,k)|) e 
yj s 
6, (A, k) and e| ó (A, k) |) are defined as: 
1405, 5,)-4(9,.Qu)| 
dis(P., P,:Q,,Q,,) 
where: d(P,D) «|| P.— P, || » the Euclidean distance 
between P and P Us 
d(Q;,Q,) = I Q, — Ou | , the Euclidean distance 
between Q, and Op : dist(P, ; Pp, ; Q, 5 Q,;, ) is the average 
distance of the two pairing, that is 
8, (hk) = drôle ‘ 
     
   
   
  
   
  
    
    
   
    
       
   
    
   
    
   
    
   
      
  
    
    
   
     
    
    
   
    
   
    
    
    
    
   
   
    
   
  
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