International Archives of the Photogrammetry, Remote Sensing and Spatial Information
2.3.2 Ring Analysis
Spatial analysis of the surrounding area of each object is
performed by dividing the area into rings around the minimal
circumscribing rectangle (Doytsher 1988). The ring analysis
method is based on giving a larger weight to rings closer to the
object. It describes the effect of surrounding objects and the
importance of the distance between them. We thus started with
the ring closest to the minimum rectangle circumscribing the
object. The effect of each ring on the density determination is
calculated as follows:
Figure 2. Ring analysis method
AW,
(8) Density 2 9 — ——————
2 ring area, > Wi
Where:
A is the area of the objects contained in the ring
W isthe weight of a certain ring
This equation, when used in the example below, produces the
required results, where objects in the middle of a given area
have higher density values than objects on the boundaries of this
given area.
Figure 3. Density values of set of buildings
In order to be more precise about the way the objects are
scattered in a given ring, the rings were divided into four parts
with the free area and the minimum distance between other
object are calculated in each part. The following examples
demonstrate the need for such sub-analysis method:
F
|
|
|
|
|
|
LA
p
Figure 4. Side analysis
Each object and its minimum circumscribing rectangle is
analyzed as demonstrated in Figure 5.
1000 1050 1100 159 1200 1250 “1200
Figure 5. Ring analysis by 4 different sides
It was found that the width of the rings should be defined as
identical to the cartographic tolerance based on the scale of the
desired map. The number of the rings is a function of the rings’
width and the area of the surrounding free region for each
object.
Rings _ area = object _area + object _ free _ surroundin _ area
Rings _ area = (ab + 2% Rings _ number * rings _ width)"2
ab=(a +b)/2
X Rings _ area — ab
(6) Rings _ number = —
e
It was found by several experiments with a satisfactory result.
that according to this equation the number of required rings
around each object is almost the same. Thus, more or less the
same weight was assigned to each of the rings surrounding the
different objects. :
a, = Rings _ number
Mia, =1
i
first ring wieght =
n
Da,
j^!
3. METHOD OF PERFORMANCE
Several requirements must be fulfilled in the generalization
process. A possible framework for automatic generalization is
to formulate these requirements as constraints and let them
control the process (Beard, 1991). The major difference
between rules and constraints is that the rules state what is to be
done and constraints state what results should be obtained
(Harrie, 2003). Since it is difficult to formalize the
212
Sciences, Vol XXXV, Part B4. Istanbul 2004
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