In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Voi. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
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The algorithm used for feature weighting was the ReliefF (Liu 
and Motoda, 2008); features with highest weights are Ah, Ap 
and NDVI; GBR and NIR have low weights; the goodness of 
selection is also demonstrated by the obtained results varying the 
set of features in the classification phase. The Weights obtained 
by the ReliefF algorithm are shown in Fig. 4. 
Weighting of features for selection 
Features 
Figure 4: Results of ReliefF algorithm applied to the set of seven 
features; the n parameter represents the number of nearest in 
stances from each class. 
Analyzing the weight of each feature, it is evident as the LiDAR 
features Ap and Ah and the NDVI have the higher values; pure 
radiometric features do not allow to classify data correctly due to 
the lack of spectral separability. 
3.2 Thresholding Normalized DSM 
Thresholding Normalized DSM is a simple technique that allows 
to classify LiDAR data; only few objects can be extracted, mainly 
buildings. Problems which afflict this approach are the ambiguity 
of high density canopies and the impossibility to distinguish be 
tween land and grass. nDSM is defined as the subtraction of the 
DTM from the DSM of the same scene. A normalized DSM con 
tains objects on a plane of height zero. Assuming that buildings 
in the scene have a known range of height, and that the heights of 
all other objects fall outside this range, buildings can be detected 
by applying appropriate height thresholds to the nDSM. 
3.3 AdaBoost 
AdaBoost (short for ’’adaptive boosting”) is presently the most 
popular boosting algorithm. The key idea of boosting is to create 
an accurate strong classifier by combining a set of weak classi 
fiers. A weak classifier is only required to be better than chance, 
and thus can be very simple and computationally inexpensive. 
Different variants of boosting, e.g. Discrete AdaBoost, Real Ada 
Boost (used in this paper), and Gentle AdaBoost (Schapire and 
Singer, 1999), are identical in terms of computational complex 
ity, but differ in their learning algorithm. The Real AdaBoost 
algorithm works as follows: each labelled training pattern x re 
ceives a weight that determines its probability of being selected 
for a training set for an individual component classifier. Starting 
from an initial (usually uniform) distribution Dt of these weights, 
the algorithm repeatedly selects the weak classifier ht (x) that re 
turns the minimum error according to a given error function. If a 
training pattern is accurately classified, then its chance of being 
used again in a subsequent component classifier is reduced; con 
versely, if the pattern is not accurately classified, then its chance 
of being used again is raised. In this way, the idea of the algorithm 
is to modify the distribution D t by increasing the weights of the 
most difficult training examples in each iteration. The selected 
weak classifier is expected to have a small classification error on 
the training data. The final strong classifier H is a weighted ma 
jority vote of the best T (number of iterations) weak classifiers 
h t (x): 
H (x) — sign ottht (x) J 
It is important to notice that the complexity of the strong classi 
fier depends only on the weak classifiers. The AdaBoost algo 
rithm has been designed for binary classification problems. To 
deal with non-binary results we used a sequence of binary clas 
sifiers, where each element of such a sequence determines if an 
example belongs to one specific class. If the binary classifier re 
turns a positive result, the example is assumed to be correctly 
classified; otherwise, it is recursively passed to the next element 
in this sequence; this techniques is known as ’’one against all”. 
As weak classifer in this paper, a Classification And Regression 
Tree (CART) with three splits and T = 35 was used. 
The CART method was proposed by (Breiman et al., 1984). CART 
produces binary decision trees distinguished by two branches for 
each decision node. CART recursively partitions the training data 
set into subsets with similar values for the target features. The 
CART algorithm grows the tree by conducting for each decision 
node, an exhaustive search of all available features and all possi 
ble splitting values; the optimal split is determined by applying 
a well defined criteria as Gini index or others ones (Duda et ah, 
2000). 
3.4 Classification Results 
In order to extract objects of interest from the previous described 
dataset, all the data were classified. In Fig. 5, the best result 
(in terms of detection rate) of classification using AdaBoost is 
shown. Moreover to evaluate correctly the quality of classifica 
tion, a ground truth for buildings was manually created (see Fig. 
6); the ground truth for the remaining classes actually is not avail 
able but it is planned to cover all the area to analyse exactly the 
classifier performance. 
Figure 5: Results of classification using AdaBoost and the train 
ing set of 32 polygons; red stands for building, yellow for tree, 
blue for land and green for grass 
In Table 1 the results for building extraction with different sets 
of features are highlighted; according to the weighting algorithm,