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)} >