International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
- (b) “building periphery”: it corresponds to the close 
neighbourhood of the building. It includes all the pixels that 
refer to the transition between the building and its close 
neighbourhood. Thus, a two pixels width zone, located from 
both sides of the building limits (i.e. around the "building 
body") can be defined ( figure 1). 
Figure 1 shows a 15 by 21 pixels "search zone" used to 
discriminate the buildings of 13 by 19 pixels (the subdivision in 
four zones of the "building periphery" is explained in the 
following sections). 
  
side 1 ; mask 1 
b? *7 true building borders [ ] 
u 
mum 
E side 2 ; mask 2 
A\\| “building periphery” 
“building body” side 3 ; mask 3 
side 4 ; mask 4 
  
building centre 
  
Figure 1. "search zone" definition 
The size and the shape of the building body and of the building 
periphery should be adapted to the real size of the building to 
discriminate. Thus, this building detection approach requires as 
many "search zones" sizes as the different real building sizes 
presented on the image. 
2.3 Quantification of grey level variations 
Various parameters can be used in order to quantify grey level 
variations for a searching window (data range, interquartil, 
variance). The variance, defined in the equation (1) is used here 
because it takes into account all the pixels of the window. 
= 1) 
(X1,j- X)2 
Vei MN 
= = 
Where: 
i and j : row and column pixel index 
M and N : row and column size of the window 
Xi,j : value of the pixel at position (i, j) 
X : mean value of all the pixels in the window 
922 
This variance can be calculated in different window sizes. Our 
goal is to quantify the local grey level variation inside a small 
zone (building body, building periphery) Thus, a minimum 
window of 3 x 3 pixels is chosen. 
2.4 Quantification of the spatial distribution of grey level 
variations 
It is necessary to quantify the spatial distribution of grey level 
variations. The goal is to discriminate a spatial distribution 
characteristic of a building to an other spatial distribution. 
The notions of "building body" and “building periphery" 
previously defined, are used here. The spatial distribution of 
grey levels variations of a building could respond to the 
following three principal requirements: 
* A low variance value for the pixels corresponding to the 
*building body". This variation can be quantified by the mean 
variance of the “building body”. 
* A high variance value for the pixels corresponding to the 
“building periphery”. This variation can be quantified by the 
mean variance of the “building periphery”. However this 
requirement is not sufficient to describe completely the variance 
value of the close building neighbourhood. Indeed, it does not 
take into account the variance repartition between the different 
building borders sides. To resolve this problem, a new condition 
is added: the variance value must be uniformly distributed 
on the greatest possible number of “building periphery" 
sides. In order to quantify this additional requirement the 
"building periphery" is subdivided in four zones, corresponding 
to the four building sides (sides 1, 2, 3 and 4 in figure 1). Then, 
the mean variance is extracted from each side and the results are 
multiplied by each order. This multiplication increases the total 
"building periphery" variance value in the case of a uniform 
distribution, and decreases the total “building periphery” 
variance value when the high variance is concentrated on a 
restricted number of sides. The result of this multiplication is 
then put on a forth-square root in order to get the same range of 
variance value as the “building body” (numerator equation 2). 
e The variance values of the building body and of the 
building periphery should be taken into account jointly. This 
is carried out by a simple division of the mean “building 
periphery" variance by the mean “building body” variance 
(equation 2). 
Spatial distribution of grey level variation of a building and its 
close neighbourhood is finally quantified by a unique parameter 
described in equation 2. This parameter is called 
"Discrimination by Ratio of Variance" (DRV). 
  
YMeanVarS 1)*(MeanVarS2)*(MeanVarS3)*(MeanVarS$4) 
  
DRV= 
MeanVarBody 
(2) 
Where: MeanVarS1, 2, 3 and 4: mean variance on the side |, 
2, 3 and 4 
. ~ ‘ . . » 
Mean VarBody: mean variance of the “building body 
According to our definition, a building usually shows a high 
variance of a minimum number of sides and a low variance of 
the body. That will result in a strong DRV value. So the DRV 
value could be used to discriminate buildings from other land 
cover types. 
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