7A-1-4 
Once the match pairs are determined, object coordinates of 
feature points can be computed. The transformation between the 
object coordinate system and the photo coordinate system can be 
achieved by using the collinearity equations (Eq.9). 
x =x r m n(X -X c ) + m n (Y-Y c ) + m l3 (Z-Z c ) 
p ° J m 3l (X-X c ) + m 32 (Y-Y c ) + m 33 (Z-Z c ) 
= m 21 (X - X c ) + m 22 (Y -Y c ) + m 23 (Z - Z c ) 
P 0 m 3l (X-X c ) + m 32 (Y-Y c ) + m 33 (Z-Z c ) 
Fig. 5 is an example of the results from feature matching on an 
epipolar line. 
4 Signal Matching 
The signal matching is driven from the object space. The problem 
is approached by dividing a terrain surface into a 2D horizontal 
array or grid. The objective of this signal matching process is to 
determine elevations of these grid points. The concept of dynamic 
programming for a line following is applied to find the optimal 
elevation profile between two end points of a grid line. 
This matching method determines the best location of the 
conjugate image points along the projection of vertical line 
segments as in the VLL method. To evaluate the match value, the 
ray from the point at a tested elevation is projected back to the 
conjugated images. At each point on a grid line, costs associated 
within a discrete set of elevations are computed from the match 
value and inserted into a cost matrix. After applying this step to 
all points on a grid line, an image of the approximated elevation 
profile can be inferred from the white path in the cost matrix (Fig. 
6). 
The optimal elevation profile in a cost matrix image is extracted 
by dynamic programming. Most signal matching methods select 
the best matches from local maxima in the similarity values. That 
approach sometimes produces false matches. Dynamic 
programming looks at the problem globally (at least within a 
profile). Therefore its solution is globally optimal. The proposed 
technique was originally designed for tracking a line which 
minimizes the sum of costs encountered while going from the 
starting point to the ending point of a network. This is similar to 
our application but we wish to find only the optimal path that 
always moves forward. Using the recurrence relation (Eq.10), the 
minimum cost required to go from point (x, y) to the ending point 
can be expressed as follows: 
will find the best one. This integration of feature matching and 
signal matching then can improve the chances that 
• The correct optimal path will be obtained. The search 
technique makes use of the benefit from features. 
• The consistency checks for feature matching can be 
accomplished. 
• For most good feature matches, there is at least an accessible 
path to the point. 
Once the optimal profiles from all gridlines are obtained, the 
object surface model can then be reconstructed. 
Figure 7: Left and right images of Bishop project 
Figure 8: Extracted edges overlaid on the original images 
f(x,y) = min 
c(x,y,x-l,y) + f(x-l,y) 
c(x, y ; x -1, y +1) + f(x -1, y +1) 
c(x,y,x,y + l) + /(x,y + l) 
c(x, y,x +1, y +1) + f(x +1, y + 1) 
c(x,y;x + \,y) + f(x + \,y) 
(10) 
During the optimization process, the object coordinates from 
matched features are used as constraints. The search technique is 
forced to pass these features by providing very small costs to any 
pixels representing 3D feature points. Although our feature 
matching algorithm is based on the optimization, incorrect 
matches are still possible. If we combine features into signal 
matching by a constraint that an optimal path must pass through 
feature points, a result may be worse than the one without 
constraints. Our approach only compels an optimal path to pass 
those matched features. It is not required to go through the points. 
If the elevations of feature points are obtained from incorrect 
matches, there would not be a good path to those points. The 
incorrect path can then be avoided. However, if there are some 
possible paths to reach a good feature point, the search technique