# Full text: Proceedings International Workshop on Mobile Mapping Technology

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

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