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Figure 5. Examples of image patches used for initial tests (a)
building examples, (b) patches not containing
buildings
these varied from case to case (Papageorgiou, 2000). As an
extension to the initial testing, a further series of tests were
performed using the small test set to determine which
preprocessing methods produced the best results. The issues
investigated included:
* The resolution level of the wavelet coefficients (32 x
32 pixels, 16 x 16 pixels or 8 x 8 pixels)
* The use of over-sampled or standard wavelet
coefficients
e The use of normalised image or raw images
* The use of wavelet coefficients or standard colour
values (or a combination)
* The use of single resolution or multi-resolution data
The various combinations of these parameters, together with
both a linear and polynomial kernel in the SVM classifier,
resulted in 216 separate tests. As expected, many of these tests
produced poor results. Those that produced successful results
were ranked according to the predicted generalization error, the
number of training errors, the number of iterations and kernel
evaluations taken to reach a solution and characteristics of the
high dimensional feature space used in the solution. This
resulted in 22 parameter sets that warranted further
investigation with a larger training set.
S. LARGE TEST SET
To expand the training data, a new data set was created from
the same photography. This dataset contained 1624 examples,
with 974 building patches and 650 non-building patches. To
validate the training, this data was split into a training set of
452 building and 354 non-building patches and a testing set of
522 building and 296 non-building patches. To generate a
richer set of data and to incorporate different building
orientations into the training, new image patches were
generated from the original set by rotating each patch through
90, 180 and 270 degrees and by mirror reversing the images
horizontally and vertically. This generated five additional
images for each patch and increased the training set to 4836
images and the testing set to 4908 images.
The SVM was trained using the training data and then the test
set was classified using this training model. This process was
undertaken separately for all 22 parameter sets identified in the
earlier tests. Several tests achieved good results, while five of
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
the tests failed to reach a solution. The results of the successful
tests are shown in Table 1.
To further evaluate the result of this training, 57 additional
building examples (342 test cases) were produced from a range
of public domain sources (Figure 6). These included the
Avenches and Hoengg datasets, colour infrared photographs
(courtesy of ISTAR Corporation), large scale photographs of a
nearby country town and screen copies of a photomosaic of
Sydney, Australia. The quality, resolution and scale of these
images varied considerably. To meet the requirements of the
software, the image patches were re-sampled to 256 x 256
pixels. These images were then used as additional test data for
the best of the classifications derived earlier. Although no
additional training was undertaken, the classifier identified
more than 65-8076 of the patches correctly, depending on the
classification method used. The majority of the errors occurred
with the Sydney images, which were of poor quality compared
to the others.
él
Figure 6. Examples of additional test images
6. DISCUSSION
All methods that established a classification were able to
produce quite good results on the out-of-sample data and
showed that the predicted generalization error from training is
somewhat pessimistic. This is consistent with other work that
has shown these estimators generally underestimate the true
accuracy (Joachims, 2000; Duan et. al., 2003).
From Table 1, it is difficult to determine a parameter set that is
clearly superior to all others. However, some general trends
emerge. The tests with suffix *b' used a polynomial kernel and
generally produced better results than those with the linear
kernel (suffix ‘a’). Test 2 7b, 3 7b and 4 7b all produced
quite good results. The only parameter to vary between these
tests was the method of normalization of the image content.
The first was normalized in the wavelet domain, the second in
the image domain and for the third, no normalization was
performed. These tests were all at the mid-range resolution (16
x 16 pixels) and used multi-resolution data.
Tests with the prefix ‘6’ were all at the coarsest image
resolution of 8 x 8 pixels and although some of these tests
produced good results, they generally required many more
kernel evaluations and are therefore more computationally
intensive. Test 6 8a produced the best results in terms of
correct building classifications but this was at the cost of more
errors in the non-building patches (false-positives) and a very
large number of kernel evaluations.
It is clear from Table 1 that good classification results are
possible using the polynomial kernel. The method of pre-
processing appears to be less important but does influence the
efficiency of the computations. One factor that is not apparent
from the table is the size of the coefficient files. The training
and testing data sets varied in size from about 10 Mbytes up to
several hundred Mbytes, depending on the resolution level, the
over-sampling strategy and whether colour image coefficients
were included in the output.
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