Dimitris Skarlatos
template is too big will not be correct. Therefore this method was abandoned because of the large percentage of Wrong
matches.
The best way to get information about the signal and content of a given template is statistical analysis. The most
common statistical measures that can be used for such analysis are the mean, standard deviation, median, mode, range
and mean deviation (Kennedy, Neville, 1976). The analysis is being done around the pixel of interest only in one image
(i.e. the left one), because we expect the search window on the other image to have the same content as well.
In order to avoid the initial approximation problem, a pair of orthophotos (from left and right photograph) was created
with 0.5 pixel size from 1:15000 scale photography over the suburbs of Volos in Greece. From the two orthophotos
three pairs were selected so that they contain a variety of features, basically homogeneous areas, edges and houses. Of
course the orthophotos created from left and right photographs are not exactly the same allowing the algorithm to work
in sub-pixel matching. Some errors in DEM produced obvious distortions in the orthophotographs, where matching
should fail. Some other features such as cars in roads should also be considered possible failures.
In order to examine the statistical measures and the best template size for matching that they suggested, a large number
of sample points were collected from the test areas (Fig. 1)
Figure 1. The three test areas with pixel size of 0.5 m. The characteristic points selected with the 41x41 template can be
viewed. The original photographs of 1:15000 scale was scanned at 600 dpi.
From the three areas 99 representative points were selected, containing a variety of features such as homogeneous areas,
line features (roads of variable widths and ploughed land), point features (trees and bushes in fields), and random
formations. The sample is big enough to export confident results. The statistical measures from 5x5 to 41x41 template
sizes were collected and diagrams were drawn in order to detect any obvious correlation between the measures and the
"correct" template size. All 99 samples were visually checked and the best template was subjectively selected and
marked. Correlation coefficient was also used so that a measure of the goodness of the template was available, apart
from the subjective criteria. Three sample areas can be viewed in figure 2.
It is quite clear that finding criteria among the 6 lines, which could be applied in all 99 cases and expressing them with
logical functions is extremely difficult. There are numerous thresholds that could be applied (i.e. when standard
deviation is more that 30) and numerous combined functions (i.e. intersection between median and mode). Another
puzzling factor that was whether there should be a penalty function for the size of the template so that to keep it to a
minimum.
The algorithm that was finally adopted was quite simple: the intersection between range and mean. If this is not fulfilled
for the 41x41 template then the standard deviation is checked against a given threshold and finally the range is checked
against the augmented mean in the certain template size. If none of the above criteria is fulfilled then no attempt for
matching is being done and the next point is selected.
The results of the aforementioned algorithm produced quite satisfying results, which could be seen in figure 3. It is clear
that the templates are bigger in homogeneous areas, while in areas with enough signal the template is kept small. In
cases where the initial point is in homogeneous areas but close to some characteristic the template is just big enough to
enclose the additional signal.
The intention to find a penalty function, so that to keep the template to a minimum (for better localization) wasn't
utilized because of the good results. All successful matches were correct, wrong matches were avoided without any
further changes to the algorithm. This phenomenon could be explained by the fact that homogeneous areas are generally
flat, and therefore the affine transformation can model the perspective geometry quite well. In sudden slope changes
there is also change in illumination, hence the algorithm keeps the template small and the affine can still model
adequately the geometry. The ratios of successful matches to attempts were 88.6%, 86.7% and 88.46% respectively.
The ratio of correct to successful matches is 100%. There might have been correct matches that haven't passed the
criteria of template size or have exceeded the iteration threshold without convergence.
846 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
