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Create voronoi diagrams (polygons) using the vertices
of buildings and blocks. and combine them if they
intersect with the buildings in same cluster. In case a
voronoi polvgon contains two buildings in different
clusters. then divide the polygon.
Compute voronoi density, i.e. the ratio of total area of
single buffers of buildings at same cluster and area of
voronoi polygon.
Check block density, if very dense(>%90), copy block
as settlement area.
Find close buildings to settlement area, check voronoi
density of the polygon which the clusters of buildings
are within and if the density >= 55% and the number of
remaining buildings in the cluster <= 2 then aggregate
(re-classify and amalgamate) all buildings in the cluster
with the settlement area, otherwise aggregate only close
buildings with it. Remaining buildings will be typified if
their shapes are similar otherwise amalgamated or
displaced (see next step).
Simplify settlement areas. ^ Aggregate holes with
settlement area.
Check voronoi density of each polygon in the blocks
(Figure 2) and displace if the density « 5596, otherwise
typify or amalgamate. Typification distance = 35 m
(minimum symbol granularity / 2 + minimum separation
distance — 1:50K) if 55% <= density < 90%,
typification distance = 35 * Jvoronoi density [90 if
density >= %90. What will happen in neighbouring
polygons may sometimes have effect on decisions but
not considered here.
Figure 2. Density of voronoi polygons (voronoi_density)
Apply amalgamation if the clusters have buildings with
different from square or rectangle. Before
amalgamation, orientations of buildings can be checked
and small ones may be perpendicularly or parallelly
rotated from its nearest point to the other building if
their orientations are rather different or if it does not
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
intersect another building after rotation. This is another
point that will be considered later.
Before typification, check the cluster homogeneity
according to shape and size. Buildings are mostly
typified if their shapes are square and sometimes
rectangle. Latter was not considered in the study, but
average size may be determined using area and
elongation, and typification distance can be computed. If
the shapes are different from square or rectangle, re-
create the clusters including similar shapes. We do not
change parameter or voronoi polygon here. This might
be considered before clustering we can then not have
direct. information about conflicts if they are in a
separate polygon. In the situation we preferred, the
buildings important from semantic and/or geometric
aspects will be given priority. In case of over density,
unimportant buildings with different semantic meaning
may be eliminated. This was also not considered in the
study.
Collapse relevant buildings, namely change their
geometry to point. Hierarchical clustering by
dendrogram is done using collapsed (changed to points)
buildings before typification (Figure 3). The
dendrogram is built by repeatedly finding the two
closest points (according to typification distance) being
considered by the process, adding them to the tree,
creating a new node to represent the cluster defined by
the two new nodes. This new, average node is then
added back into the pool being considered for finding
the closest pair. In this way, the number of nodes in the
pool is always reduced, as two are replaced by one
(Laser-Scan, 2001).
Figure 3. Clustering of buildings using dendrograms
Then, they are typified using mean points (average
coordinates) (Figure 4). After typification, building
symbols are rotated parallelly to the nearest road. In this
case they may be close to each others. To prevent this,
nearest distances among building polygons instead of
points need to be considered, however this can possibly
get the strategy more difficult.