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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
K(x,x) - 2'£ i ajk{x,x i ') + y £a i a j K(x j ,x j ) < R 2
(9)
Two types of kernels are often used: polynomial and Gaussian
kernels, however, the former usually does not produce a tight
description of the data and is sensitive to outliers when the
polynomial degree is high (Tax and Duin, 1999a). A more
robust way is to construct the Gaussian kernel, which has been
commonly used for one-class SVMs (Tax and Duin, 1999a;
Scholkopf et al., 2001):
K( x i ,x j ) = e~ (XrXl?ls ' (10)
where S is the kernel width. The Gaussian kernel was applied in
this study. It should be noted that the method above was
proposed by Tax and Duin (1999), another approach proposed
by Scholkopf et al (1999) is to find some hyperplane to separate
the training data from the origin with the maximum margin. For
the Gaussian kernel, these two methods are equivalent
(Scholkopf et al., 2001). We implemented the one-class SVMs
by the modified version of LIBSVM-a library for support vector
machines developed by Chang and Lin (2001). A more detailed
mathematical derivation of one-class SVMs can be found in
Scholkopf et al. (1999), and Tax and Duin (1999a). In this
study, both Gaussian kernel width (5) and V are estimated from
the cross validation method that maximizes the classification
accuracy (i.e. Kappa value).
2.2.6 One class SVMS with pixel-based classification: as a
comparison, we implemented the one class SVMs with pixel-
based classification. Features used in pixel based classification
include digital values of three bands for each pixel. In order to
catch the texture information in the classification, we also used
the variance of digital value for each pixel with a 5x5
processing window in each band. As a result, six features are
used in one-class SVMs with pixel-based classification. The
training samples and testing samples are used similar to the
object-based method. The major difference is from the
perspective of data storage and processing: in the object-based
method, the segmented objects as well as training and testing
samples are stored as polygons and hence processed in the
vector format, while, in the pixel-based method, the data are
stored and processed in the raster format only.
3. RESULTS
For the one-class SVMs with object-based method, we found
that the combination of shape index and mean difference to
neighbour provided the highest Kappa score based on the five
fold cross validation method. Kappa value is 0.79. The kernel
width and the v for one-class SVMs are 0.03 and 0.06
respectively. The final classification result is shown in Figure 3.
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Figure 3. one-class SVMs with object-based classification. The
pink objects are houses, and blue objects are non-houses.
For the one-class SVMs with pixel-based method, the kernel
width and the v for one-class SVMs are 0.07 and 0.02
respectively by using the brute-force search method. The
optimal Kappa value for the classification is 0.30. Figure 4
shows the final classification result based on one-class SVMs
with the pixel-based method. This method can effectively
distinguish houses from grasslands, but it is difficult to
distinguish houses from roads.
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Figure 4. Classification results based on one-class SVMs with
the pixel-based classification. The pink objects represent houses
and the gray objects represent non-houses.
4. DISCUSSION
The result indicates that one-class SVMs with the object-based
classification (kappa = 0.79) outperformed the pixel-based
counterpart (kappa = 0.30). Two reasons may contribute to the
differences:
1) The object-based classification can provide more meaningful
candidate features such as shape and mean difference to
neighbour, which is very useful in differentiating houses from
roads. Because of the spectral similarity between houses and
roads, conventional pixel-based methods are difficult to
distinguish between them as shown in Figure 4.
(2) Since the pixel-based classifies the image pixel by pixel, the
final classification is very fragmented, particularly in
classifying high spatial resolution images. As shown in Figure 4,
many pixels are misclassified as houses. Based on the shape
and size of those pixels, we could easily tell that they are not
houses. Therefore, in order to make use of the classification
result from pixel-based methods for extracting houses from high
resolution images, users normally need to manually or semi-
manually post process the classified image. On the other hand,
the object-based method seeks to first segment the images based
on spectral similarity among pixels, and then classify the
images based on features extracted from the segmented objects.
The classification results are much smoother and almost ready
for environmental or urban applications (Figure 3).
In sum, with the increasingly available high spatial resolution
imagery, one-class SVMs together with object-based
classification methods provide a promising way in extracting a
specific land class type from high resolution images.