The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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meaningful information from these regions, we need to segment 
such areas occurring in the images. 
The heterogeneity and the geometrical complexity of urban 
structures in low radiometric and mid-resolution (2m or 5m) 
images show textural effects for objects with few pixel width. 
In our study we use the work of (Roux, 1992) developed to 
extract the urban regions from SPOT images. In SPOT images, 
the urban zones appear to be strongly textured and the problem 
of extraction of the regions is essentially a problem of 
differentiation of textures. The method used here is inspired 
from the works of (Serendero, 1989) and (Khatir, 1989). The 
principle idea is to extract the zone of high density of light and 
dark peaks. The techniques used are of mathematical 
morphology operations of opening and closing. The segmented 
compact urban regions in the images are shown in Figure 3(b) 
and Figure 3(d). 
(c) Original image © ONES (d) Segmented region 
Figure 3: Images containing small urban areas and their 
segmentations. 
2.2 Road Network Features 
useful measure to separate urban and rural areas: we expect 
urban areas to have a higher value of Nj and Ej than rural areas. 
Similarly, we define the ‘network length’ L = l e and the 
‘length density’ to beZ = ET X L . Again, we expect urban areas 
to have a higher value of L than rural areas. Note than one can 
have a high value of L and a low value of Nj if junctions are 
complex and the road segments are ‘space-filling’. We also 
compute the network area Cl L as the number of pixels 
corresponding to the network from the extracted binary image 
and define the ‘network area density’ as A = if 1 Q. L . As can be 
seen in figure 2, many junction points are clustered around a 
small area in the network. To obtain a local characteristic of the 
junction density, we define a measure called ‘local 
junction’: N r , =Q7 J r > 1 . This is the density of 
rJ J ’ r ¿—¡ven. jr ,m v > 2 
junction points falling in a circular region of radius r centered at 
junction point j. We then compute the mean and the variance of 
these junction densities over all junction points, mean(A r</ ) and 
var(N rj ). A high v'dr(N rj ), indicates the sparse structure of road 
junctions. Rural network structures will show such a 
characteristic. A low value indicates that junction points are 
clustered close to many other junction points, which is a 
prominent measure of urban network structure. The mean(Jv ri/ -) 
is also used as a measure of density. 
Let p e = l e / d e , and k e = l e 
^|cw/*v($)| 
ds , i.e., the absolute 
curvature per unit length of the road segment corresponding to 
the edge e. Although it may seem natural to characterize the 
network using the average values per edge of these quantities, 
in practice we have found that the variances of these quantities 
are equally useful. We thus define the ‘ratio of lengths 
variance’ and the ‘ratio of lengths mean’ to be the variance and 
mean of p e over edges, var(p) and mean(p), and the ‘average 
curvature variance’ and ‘average curvature mean’ to be the 
variance and mean of k e over edges, var(&) and mean(&). Note 
that it is quite possible to have a large value of p e for an edge 
while having a small value of k e if the road segment is 
composed of long straight segments, and vice-versa, if the road 
‘wiggles’ rapidly around the straight line joining the two 
vertices in the edge. We expect rural areas to have high values 
of one of these two quantities, while urban areas will probably 
have low values, although this is less obvious than for the 
density measures. 
In this section we focus on 16 features summarized in table 1. 
These features can be categorized into six groups: six measures 
of ‘density’, four measures of ‘curviness’, two measures of 
‘homogeneity’, one measure of ‘length’, two measures of 
‘distribution’ and one measure of ‘entropy’. We will now define 
the road network features. 
Let v be a vertex and e be an edge. Let l e be the length of the 
road segment corresponding to e, and let d e be the length of e, 
that is the Euclidean distance between its two vertices. Let m v 
be the number of edges at a vertex. Then N, = / 1 is the 
number of junction vertices and Ej = / m v is the number 
¿—¿m v >2 
of junction edges. Let Q be the area of the image in pixels. We 
define the ‘junction density’ to be N j =Q.~ l Nj and ‘density of 
junction edges’ to be Ej-OT^Ej. These are intuitively a 
To measure network homogeneity, we divide each image into 
four quadrants, labelled a. Subscript a indicates quantities 
evaluated for quadrant a rather than the whole image. Let 
M Ja = / m v be the number of edges emanating from 
’ vea,m>2 
junctions in quadrant a. This is very nearly twice the number of 
edges in a, but it is convenient to restrict ourselves to junctions 
to avoid spurious termini at the boundary of the image. Let 
M Ja =QT x M Ja be the density of such edges in quadrant a. 
Then we define the ‘network inhomogeneity’ to be the variance 
of Mj a over quadrants, var( Mj). We also include 
mean( Mj) as a feature. 
In order to distinguish between the two urban classes (USA and 
Europe), the entropy of the histogram of angles at junctions, Hp, 
where is the vector of angles between road segments at 
junction j, is a good measure. As is evident from the physical