ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
ISPRS, Vol.3‘
3.4.1 Distribution density
For generalization application, the building distribution density
supports operation decision from macro perspective. In
partitioning model, the description of building distribution being
dense or sparse depends on the rate of OP area to GP area. The
denser, the smaller room one building gets during competing
outward, and the more similar of GP size to OP size. So this
area rate ranging from 0 to 1.0 is able to represent building
distribution density. Figure 5 is an example of this kind of density
representation. The region is shaded with gray scale proportional
to the rate of OP area to GP area.
Fig. 5. An illustration of representation of building
distribution density, the region shaded with grey
scale proportional to the rate of OP area to GP area.
3.4.2 Adjacent Distance
In building cluster, the adjacent degree between two buildings
can not simply be described as minimum distance, such as in
Figure 6. What it means for A to be near B depends not only on
their absolute positions(and the metric distance between them),
but also on their relative sizes and shapes, the position of other
objects, the frame of reference (Hernandez and Clementini,
1995). The context environment plays an important role.
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A
Fig. 6. The minimum distance is same, but C is
closer to A than B in visual cognition.
Based on partitioning model, applying differential idea we give
the following method to compute distance between two buildings.
k 11P; R +i "
w-
s
IWiVfcl
Type I Type II Type III
Fig.7, W,W 2 , skeleton width representation for 3
types of triangle
Fig 8. Neighbor C moving and rotating leads to the
distance change between building A and B based
on the weighted skeleton width computation..
A GP boundary edge relates two adjacent OPs and goes across
a set of triangles which divide the skeleton into segments. For
each short segment, compute this local distance between OPs
according to triangle type and then integrate the local distance
weighted with the rate of local segment length to the whole
skeleton length. For three types of triangle, the local skeleton
width representation, WiW 2 is expressed in Figure 7. The
computation function is where / the whole skeleton length, k the
number of involved triangle, w is also called skeleton width.
This weighted distance computation based on skeleton takes
into account the building shape structure, spatial distribution and
other building’s influence. In Figure 8, building A and B keeps
unchange and C moves and rotates, resulting in the distance
between A and B decreased. In visual cognition, we can feel in
the right A and B are closer than that in the left due to C position
change. For Figure 6, this weighted distance computation will get
the adjacent relation between A and C is closerer than that of A
and B. So this distance computation is consistent with visual
cognition in some degree.
3.4.3 Adjacent Direction
An approximated direct line can be computed for one skeleton
using Least Square Adjustment method, and the normal line
direction can be regarded as the adjacent direction between two
adjacent buildings. Adjacent direction will be used in next section
for building displacement.
4. APPLICATION IN BUILDING CLUSTER GENERALIZATION
Building cluster generalization involves grouping, displacement,
aggregation and simplification. The partitioning model is able to
support the generalization in several aspects. From high level
decision to low level operation, this section discusses the
process on the basis of many experiments in detail.
4.1 Where Is There Conflict?
The weighted skeleton width acts as the condition of conflict
recognition. We present two conflict concepts : conflict skeleton
and conflict building. Those skeletons with weighted width
shorter than predefined tolerance are identified as conflict
skeletons, and those building objects related to one or more
conflict skeletons are defined as conflict building objects. Figure
9 gives an example of judgement of conflict skeleton and conflict
building.
9. Experiment illustrations of conflict skeletons,
visualized as wide line, and building displacement
direction, visualized as arrow line and dark dot.
According to GP connectivity, the conflict object can be assigned
into classes. This class is depend on adjacent distance, and
further grouping needs Gestalt analysis and other non-distance
assessment.
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4.2 How to Displace?