Mingsheng Liao 
  
bridge mode method as shown in Fig.1, the correlation coefficient p( ih ; jk ) between the image segment ih in the 
master image and the image segment jk in the slave image can be used as a measurement of the compatible coefficient 
Cj; hk) of O;e C; 0,e C, , ie: 
C, j;h, k) e« pCih , jk ) (2) 
After P; and C(i,j; h,k) are defined, the relaxation iterative procedure would be induced, 
Qj) - XD (ym) cj) pij) 
pij) e p "7j (1 B- Qj) (3) 
(rt): ss Di): J)p(T); ; 
pij) o PER ij) 
Here n(H) is the number of neighbor points (8- or 24-neighbourhood), m(K) and m(J) is the number of the candidates. 
The scalar B is a constant with which the convergence rate of the iteration procedure could be adjusted. The value P(r) 
determines whether the iteration is stop. Finally the reliable point pair can be confirmed if P”> T, here T is the 
threshold. 
2.3 LS Matching Procedure 
The relaxation algorithm discussed above can improve the reliability of the determination of the conjugate point. But it 
is difficult to refine the matching accuracy. It is necessary to take the further procedures. As well-known, LS correlation 
method has successfully been developed, which could achieve very high accuracy of correlation by means of 
minimization of the root mean square value of the gray value differences of the image pair. Here the principle of 
minimization of grey value differences between the two correlation windows is used instead of the conventional 
approach based on maximization of the correlation coefficient (Rosenholm 1986). 
We describe the general principle in one-dimensional case. Assume that there are two grey value functions g(x) and 
g(x) with an image pair. In an ideal case, these two functions should be the same except for a displacement x, between 
them. Their noises are n,(x) and nfx) respectively. Then the observation functions are shown as (subscript i 
representing the corresponding values at pixel i ): 
8,05) 7 8 (x; )+ my(x;) (a 
8595) 7 22(X; )t n»(;) 9 8 (xj — xo) t noGxj) 
Ag(x; ) = 8 2(X; )- £,(Xxj) 2 8i(Xj — Xo )— 8 (x; )+ny(x; )— n,(x; ) (5) 
Assume x, to be small, we linearize g,(x;x,) in the Ist order term and write equation(5) again as following: 
Ag( x )+ V(4)=-8{4)% (6) 
where v(x;)=n;(x;)—n2(x2 ) , which is the linearized error equation. The observed value is the gray value 
differenceAg(x,) . The unknown value is x,. Using the method of Least Squares, the following equation is obtained 
and value x, is thus solved: 
Yao Ya) nao) = min a) 
Practically, since each pixel pair can constitute an error equation, there are MxM observed values within a MxM 
matching window, which are redundant for the solution of x, Because the linearization exists in Fjuation (6), the 
solution has to be iterated. 
The principle can be easily generated into 2D image matching case. Herewith the initial values for the iteration can be 
obtained from the result of the relaxation matching as described in Section 2.2. Theoretically the accuracy of 
determination for conjugate points in this method may reach the order of 1/50 to 1/100 pixel. Considering other factors, 
the accuracy of 1/10 pixel for IDSAR data registration will be satisfactory . 
  
188 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 
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