The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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tween random or greedily deterministic approaches to find 
an appropriate subset of features to perform satisfying clas 
sifications. 
Alternatively, Guyon and Elisseeff (2003) propose a feature 
selection framework which is based on the ranking of fea 
tures. Then, the classification step itself is done by only one 
classifier. In our experiments, the features have low corre 
lation coefficients with the class target and they are highly 
correlated with each other. Furthermore, the training sam 
ples do not form compact clusters in feature space. Then, it 
is a hard task to find a single classifier that is able to sepa 
rate the classes. Thus, we prefer a feature selection scheme 
which combines several classifiers. 
One of such schemes is the framework of adaptive boosting 
(Adaboost), cf. (Schapire, 1990). The first weak classifier 
(or best hypothesis) is learnt on equally weighted training 
samples (x n ,y n ). Then, the influence of all misclassified 
samples is increased by adjusting the weights of the fea 
ture vectors before training the second weak classifier. So, 
the second weak classifier will focus especially on the pre 
viously misclassified samples. Again, the weights are ad 
justed once more depending on the classification result of 
the second weak classifier before training the third weak 
classifier, and so on. Finally, we obtain the resulting clas 
sifier by a majority vote of all weak classifiers. The dis 
criminative power of this resulting classifier is much higher 
than the discriminative power of each weak classifier, cf. 
(Ratsch et al., 2001). 
This majority voting is also done when using random forests, 
which are based on random decisions when constructing 
decision trees. In (Ho, 1998), a random selection of a pre 
defined small number of features is used for constructing 
decision trees. This procedure is equivalent to projecting 
the feature vectors into a space with much lower dimen 
sionality, but the projections differ from one decision tree 
to the others. The decision trees in (Breiman, 2001) ran 
domly choose a feature from the whole feature set and takes 
it for determining the best domain split. Both methods only 
work well, if the number of random decision trees is large, 
especially if there are only features which are nearly un 
correlated with the classes. In the experiments by Breiman 
(2001), decision trees were used five times more than weak 
learners in Adaboost. Therefore, we focus our work on Ad 
aboost and its variants. 
3 FEATURE SELECTION WITH ADABOOST 
The basic algorithm of Adaboost as taken from (Schapire 
and Singer, 1999) is shown in alg. 1. Input are the number 
T of iterations and N samples (x n ,y n ) with binary tar 
gets, i. e. y n £ {+1,-1}. In each iteration, the best weak 
classifier is determined with respect to the samples weights. 
Each weak classifier ht is a function h t : x n >—► {+1,-1}. 
After Adaboost has terminated after T iterations, the result 
ing strong classifier H can be depicted as weighted major 
ity voting over the responses of all weak classifiers: 
H(x n ) = sign a t h t (x n ) \ . (1) 
The a t are predictive values and depend on the weak clas 
sifiers success rates. 
Algorithm 1 Adaboost algorithm 
1: function Adaboost(T, (xi, y\),..., (xat, j/tv)) 
2: W? = i 
3: for t = 1,..., T do 
4: Determine best weak hypothesis h t using W t 
5: Determine a t 
6: Determine distribution Wt+i 
7: end for 
8: return H with H(x) = sign a t h t {x)). 
If the weak classifiers are designed in a way that they use 
only a limited set of features, e. g. 1 feature only, then we 
are able to derive the relevance of features from the rele 
vance of the weak classifiers. In the case, where only clas 
sifiers on single features are used, the strong classifier H 
consists of T weak classifiers hi,..., hr, and we obtain a 
list of maximally T features that are involved in classifica 
tion. If T < D, then these maximally T features are the 
most appropriate features for classification. 
Another strategy for obtaining the best feature subset is pre 
sented in (Drauschke and Forstner, 2008). In case T « D 
or T > D, we cannot assume to find the best subset by 
only taking those features that have been used by the first 
weak classifiers. The influence of a feature depends on the 
absolute value of the predictive values at- Since these at 
do not monotonously decrease with increasing t, we have 
to evaluate the features after the iterative process has termi 
nated. 
4 DATA 
We use terrestrial images of the eTRIMS data base for test 
ing our feature selection and classification. This data base 
contains several hundred buildings from several major Eu 
ropean cities or their suburbs. We selected 82 images from 
Berlin, Bonn and Munich, Germany, and from Prague, Czech 
Republic. 
Typically, buildings have dominant vanishing lines in hori 
zontal and vertical directions, respectively. If a pair of lines 
in the image is selected for each of both directions, we are 
able to determine the vanishing points and the homography 
for rectifying the image, cf. (McGlone, 2004), p. 775. So 
far, we work on rectified images which where the image 
rectification has been calculated after manual selection of 
these two pairs of lines. We show such a rectified image in 
fig. 1. 
Our class ontology contains several object classes, and our 
goal is to find instances of these classes in images. At this 
stage, we limit our experiments to a subset of classes. On 
the one hand, we are interested in building detection, and 
therefore, we want to classify image regions as facade, roof 
sky or vegetation. On the other hand, we are interested in 
detection of building parts, and therefore, we want to clas 
sify image regions as windows or window panes. Objects of 
both classes appear in all images, and regarding their cardi 
nality, these are the most dominant structures in all images 
of the eTRIMS data base.