In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3A/V4 — Paris, France, 3-4 September, 2009 
Here, the membership degree h for every instance x, to 
cluster j, is produced based on the Euclidean distance d: 
d(x n /jj) 
where 
fj. e <g d = cluster center. 
At each iteration, the boost-clustering algorithm clusters data 
points that were hard to cluster in previous iterations. An 
important issue to be addressed here and that is the cluster 
correspondence problem between the clustering results of 
different iterations (Frossyniotis et al., 2004). 
2.2 Feature Extraction 
The first step in every clustering process is to extract the feature 
image bands. These features must contain useful information to 
discriminate between different regions of the surface. In our 
experiment we have used two types of features: 
- The filtered first pulse range image using gradient 
- Opening filtered last pulse range image 
By our experiments, these two features have enough 
infonnation to extract our objects of interest. 
The normalized difference of the first and last pulse range 
images (NDDI) is usually used as the major feature band for 
discrimination of the vegetation pixels from the others. 
However, building boundaries also show a large value in this 
image feature. It is because when the laser beam hits the 
exposed surface it will have a footprint with a size in the range 
of 15-30 cm or more. So, if the laser beam hits the edge of a 
building, then part of the beam footprint will be reflected from 
the top roof of the building and the other part might reach the 
ground (Alharthy and Bethel, 2002). The high gradient response 
on building edges was utilized to filter out the NDDI image 
using equation 6. 
NDDI = 
FPR-LPR 
FPR + LPR 
(6) 
if gradient > threshold, then (FPR-LPR) = 0.0 
where 
FPR = first-pulse range image data 
LPR = last-pulse range image data 
The gradient of an image is calculated using equation 7: 
G(image) = ^G x (image) 2 + G y (image) 2 
where 
G x = gradient operators in x direction. 
G y = gradient operators in y direction. 
(7) 
The morphology Opening operator is utilized to filter elevation 
space. This operator with a flat structuring element eliminates 
the trend surface of the terrain. The main problem of using this 
filter is to define the proper size of the structuring element 
which should be big enough to cover all 3D objects which can 
be found on the terrain surface. The Opening operation is 
defined by: 
AoB = (AQB)®B (8) 
where 
A ® B - jx: | {¿ x n^)c= a] (9) 
is the morphological Dilation of set A with structure element B. 
And 
AQB = {x | B x <z A) (10) 
is the morphological Erosion of set A with structure element B 
(Gonzalez and Woods, 2006). 
2.3 Quality Analysis 
Comparative studies on clustering algorithms are difficult due 
to lack of universally agreed upon quantitative performance 
evaluation measures (Jain et al., 1999). Many similar works in 
the clustering area use the classification error as the final 
quality measurement; so in this research, we adopt a similar 
approach. 
Here, we use error matrix as main evaluation method of 
interpretation result. Each column of this matrix indicates the 
instances in a predicted class. Each row represents the instances 
in an actual class. All the diagonal variants refer to the correct 
interpreted numbers of different classes found in reality. Some 
measures can be derived from the error matrix, such as producer 
accuracy, user accuracy and overall accuracy (Liu et al, 2007). 
Producer Accuracy (PA) is the probability that a sampled unit 
in the image is in that particular class. User Accuracy (UA) is 
the probability that a certain reference class has also been 
labelled that class. Producer accuracy and user accuracy 
measures of each class indicate the interpretability of each 
feature class. We can see the producer accuracy and user 
accuracy of all the classes in the measures of “producer overall 
accuracy” and “user overall accuracy”. 
PA, 
f N i i} 
( N i i Ì 
—Li- * 100% . 
, UA,= — 
1 N .i 1 
KJ 
: ! 00% 
(ID 
where 
N. = (i,j)th entry in confusion matrix 
N j = the sum of all columns for row i 
N is the sum of all rows for column i. 
“Overall accuracy” considers all the producer accuracy and user 
accuracy of all the feature classes. Overall accuracy yields one 
number of the whole error matrix. It‘s the sum of correctly 
classified samples divided by the total sample number from user 
set and reference set (Liu et al, 2007). 
k 
± N u 
OA = -7——— ^ * 100% ( 12 ) 
k /=i /=1 
Another factor can be also extracted from confusion matrix to 
evaluate the quality of classification algorithms, which is K-