where mavPumitiq- 
The maximum similarity score p is 1, which means the two 
feature descriptors are exactly the same. The minimum 
similarity score is 0 which means the two feature descriptors are 
orthogonal to each other; in other words, they don't have any 
relation. PDF matching is implemented based on mean-shift 
searching strategy. Finally, affine transformation parameters are 
estimated based on the PDF-matched tie points. Note that 
RANSAC is used to remove the blunders. Figure 8 illustrates 
the co-registration results after RANSAC blunder detection; the 
RANSAC threshold value is set to 0.5-pixel. 
  
Figure 8. Co-registration result 
3.3 Extracting Smooth Bridge Boundaries in Aerial Image 
Hough linear transform is applied to the bridge ROI in the aerial 
image to extract the bridge boundaries. For each Hough 
transform identified linear feature, its Hough transform angle is 
also recorded, which can be used to determine the bridge 
direction and remove the non-bridge linear features. For a long 
curved bridge, Hough circle transform was attempted to extract 
the curved boundaries; nevertheless, the performance was not 
stable. Alternatively, short linear features are extracted along 
the curved bridge boundaries. Since Hough linear transform 
cannot be directly used to extract long curved bridge 
boundaries, the long curved bridge ROI is divided into several 
small sub-ROIs, as shown in Figure 9. 
     
(a) (b) 
Figure 9. Sub-ROIs of a curved bridge ROI (a) and 
short linear features in sub-ROI 4 (b) 
32 
Then, it is possible to obtain short linear features in each sub- 
ROI. Hough linear features in all sub-ROIs are merged together 
to form the complete Hough transform linear features along the 
long curved bridge boundaries. The endpoints of linear features 
are used to generate the smooth bridge boundary, see red points 
in Figure 10. 
It is also necessary to determine points of upper and lower 
boundaries for the smooth boundary generation. In order to 
simply separate the upper and lower boundary, all linear 
features are rotated to align to the horizontal direction based on 
the recorded Hough transform angles. This step is performed in 
each sub-ROI for the curved bridge. If the bridge is rotated to 
horizontal direction, upper and lower boundaries can be 
separated based on comparing the Y coordinate. For straight 
bridge boundary, 1* order polynomial function is used to fitting 
those boundary points; for curved bridge boundary, 2" order 
polynomial function is used. Once the polynomial function 
parameters are estimated, the smooth boundary can be then 
represented in the dense sample points computed via the 
polynomial function, see blue points in Figure 10. 
  
Se 
(b. 
Figure 10. Smooth boundary points computed via 2"* order 
polynomial function (blue) according to the Hough linear 
feature endpoints (red) 
3.4 Precise DBM Generation 
If the affine transformation between LiDAR intensity and aerial 
image is established, smooth boundaries can be transformed 
from the aerial image to the LiDAR intensity image as well as 
to the LiDAR elevation data. The upper and lower boundaries 
are shifted to best fit the upper and lower coarse boundary from 
the coarse DBM. Figure 11 shows the smooth boundaries, 
fitting the coarse boundaries. The void area between the smooth 
boundary (pink) and the coarse boundary (blue) extracted from 
LiDAR data should be filled in to form a precise DBM. In 
addition, the elevation values of the smooth boundary points are 
computed based on interpolating its neighbour points’ elevation 
values. The precise DBM can be merged with the DTM derived 
from LiDAR data to form a precise DSM. 
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