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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.