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