2 
Decision fusion can be defined as a strategy to join information 
from different data sources, after each individual source has 
been classified previously. Support Vector Machines (SVM) are 
another recent development in the field of remote sensing 
(Huang et al., 2002, Foody and Mathur, 2004, Melgani and 
Bruzzone, 2004), which is well known in machine learning and 
pattern recognition. 
SVM differentiate between two classes by fitting an optimal 
separating hyperplane to the training samples in the multi 
dimensional feature space (Vapnik, 1998). For classes that are 
not linearly separable, the input data are mapped into a higher 
dimensional space by a kernel function. 
In several experiments, the SVM achieved accurate 
classification accuracies and even performed well when applied 
to high-dimensional imagery or multisource data sets. Song et 
al. (2005) applied a “conventional” SVM to a multisource data 
set, consisting of multispectral images and topographical 
information. In other studies, the kernel functions were 
modified for classifying dissimilar data sources (Halldorsson et 
al., 2003; Camps-Valls et al., 2006). In contrast to this Fauvel 
et al. (2006) used two individual SVM classifiers to combine 
different information from hyperspectral imagery. Two SVM 
were applied separately on the original image and on a data set, 
containing spatial information (i.e., extended morphological 
profiles). Afterwards the outputs were combined by different 
voting schemes. 
These experimental results clearly demonstrate that the 
accuracy for multisource classifications can be further increased 
by using modified kernel functions or separate SVM classifiers. 
Hence, it could be appropriate to handle the different image 
sources separately when classifying multisensor data sets 
including multi temporal SAR and multispectral imagery. 
In Waske et al. (2007) individual SVM classifiers are trained on 
two separate data set (i.e., multitemporal SAR and 
multispectral). The generated pre-classifications are combined 
by decision fusion to create the final result. Beside different 
voting concepts, as a majority voting and the absolute 
maximum, fusion is performed by an additional SVM. The 
proposed SVM-based fusion strategy outperforms all other 
concepts and improves the results of a single SVM that is 
trained on the whole multisource data set. 
In the following experiment this fusion concept is applied to 
multisource imagery from an agricultural region. The 
classification results are compared to results of other algorithms 
as maximum likelihood classifier, decision tree, boosted 
decision tree and common SVM. 
2. CLASSIFCATION STRATGIES 
2.1 Support Vector Machines 
For a binary classification problem in a d-dimensional feature 
space, Xi e<R d ,i = \,2,...,L denotes a training data set of L 
samples with their corresponding class labels y i e {l,—l}. The 
hyperplane f(x) is defined by the normal vector and the bias, 
denoted by we 9^ and 6e9I respectively, where |6|/||w|| is 
the distance between the hyperplane and the origin, with ||w|| as 
the Euclidean norm from w. 
f(x) = w-x + b (1) 
The margin maximization can be defined as the following 
optimization problem: 
( L 
/(*) = 
'Yj a l y i k{ x i,x j )+b 
V '=1 
(2) 
with as slack variables that are introduced to deal with 
misclassified samples in non-separable cases. The constant C is 
added as a penalty for cases which are located on the wrong 
side of the hyperplane and it controls the shape of the 
classification boundary. Therefore, it directly affects the 
generalization capability of the SVM. 
Using the so-called kernel methods, the above linear SVM 
approach has been extended for non-linear separable cases. For 
non-linear problems, the data is transformed into a higher 
dimensional Hilbert space, using a non-linear mapping <Z>. The 
kemel-trick enables to work within the newly transformed 
feature space, without knowing explicitly O, but only the kernel 
function: 
SAR data 
/ 
ZJ 
1 / 
Figure 1. Sch 
W*. ))=*(*«,*;) 
The final decision function can be written as: 
( L 
I 
V i=l J 
/(*) = 
'Y j a l y l k{x i ,x j )+b 
where a¡ denotes Lagrange multipliers. 
(3) 
(4) 
In our study, a Gaussian radial basis function is used (Vapnik, 
1998): 
( \ 
Il il 2 * 
[Xi,Xj )= exp 
i 
1 
H 
1 
i 
The output of the decision function f(x) provides the distance of 
each pixel to the separating hyperplane, giving a rule image, 
which is used to determine the final classification result. 
The SVM was originally designed as a binary classifier. Hence 
different concepts have been proposed to solve multi-class 
(«-class) problems. In the one-against-all (OAA) approach, a set 
of classifiers is generated to separate each class from the others, 
e.g., forest from the rest, urban from the rest, etc. The maximum 
distance value within the n rule images determines the final 
class membership. For the one-against-one (OAO) strategy, a 
set of n(n-l)/2 individual SVM is trained, one for each pair 
wise classification problem, e.g., forest vs. urban. As done in 
the OAA approach, each individual SVM classifier provides a 
rule image. Contrary to the OAA approach, each pixel is 
assigned to the class getting the highest number of votes. 
2.2 Decision Fusion Strategy 
The strategy for combining the two different sensor sources is 
presented in Figure 1. On each image source a set of SVMs is 
trained individually and corresponding rule images are 
generated. The information from the rule images is fused by 
applying an additional SVM on a data set, containing all rule 
images. 
3. D/ 
The multisource 
multitemporal S. 
2005. The SAJ 
polarization anc 
polarizations (T£ 
Figure 2. S 
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used as referen 
data sets.