The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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Figure 13. Curve representation A2 
where 1 < / < m , 1 < j < n , i + j < m + n and 
c\fm, ri),{i, y)] * s cost °f primitive path between nodes 
(m,n) and (ij): 
c[(m,n),(i,j)\ 
a(m,n) • K(m,n) 
max {length of _ A, length of _B} 
Figure 14. Curve representation B2 
Next step in contours identification is to construct matching 
procedure for contours, presented in the form “curvature versus 
arc length”. 
where 
min {iPo^ (/w) - Pos A (m -1)1,1Pos B (n) - Pos B (n -1)1} 
a(m,n) = ^ 'f. ' r ’ 
max §Pos A (m) - Pos A (m -1)|,\Pos B (n) - Pos B (n -1)|} 
Pos A (m) is the position of m-th extremum in the curvature 
function of contour A; 
Pos B (n) is the position of n-th extremum in the curvature 
function of contour B; 
K(m,n) is the normalized cross-correlation value between 
local neighbourhood of m-th extremum in the curvature 
function of contour A and local neighbourhood of n-th 
extremum in the curvature function of contour B. 
3.2 Matching with dynamic programming 
The contours under investigation should be prepared for 
matching procedure beforehand (Ohta, Y., Kanade, T., 1985). 
In 1-D contour representation one finds all local extrema with 
absolute value more than threshold T, Figure 15. All these 
points present the most distinguished ones of function and 
hence they are taken further as features for matching. 
For each pair of contours A and B from first and second images 
respectively one should calculate the DP matrix and find 
optimal way minimizing the cost function. Dimensions of 
matrix depend on the numbers of extrema in two contours. 
Extrema of contour A define the number of columns M while 
extrema of contour B define the number of rows N in DP matrix. 
The cost D(A,B) of matching of contour A with contour B is 
defined as: 
D(A, B) - max(C(w, n)), 
The performance of DP-algorithm in finding the optimal 
matching solution for two contours, presented by their curvature 
functions, is shown in Figure 16, the typical size of DP matrix 
is of the order 20. The optimal way is underlined by bold line. 
As a result, DP algorithm has found 9 matched contours for 
rural images and 7 for urban ones, shown in the Figures 17 and 
18 respectively together with source images. Therefore, we can 
identify these pairs of images with high degree of confidence as 
images of the same 3D site. 
where C(m,n) , the cost of partial path from first point to node 
(m,n) is given by 
C(m, n) = max{c[(m,/7), (/, j)] + C(i, j)} >