Geography Reference
In-Depth Information
Results: Case Study
In this chapter, we highlight some typical cases, where geometry generalization was
not satisfactory according to the shape metrics measurement. We evaluated geom-
etry generalization levels by individual shape metrics values complemented with
visual comparison in particular level. We also show examples of generalized
ground plans together with shape metrics graphs for better comprehension.
Shape metrics were calculated in order to find out if the geometry generalization
process is tuning the output polygon properly. Ideally, the geometry generalization
method should simplify the polygon more and more with every single subsequent
step. In fact, the opposite is true in some cases and generalization levels. Shape
metrics values fluctuations during generalization are depicted and commented.
Nevertheless, general trend of the polygon simplification was preserved in the
sense of shape metrics values.
One of the easiest metric to obtain and interpret is the shape area. Depending on
the original shape of the building, the shape area should not decrease during the
generalization process. According to Lee and Hardy (
2006
), algorithm we used
should keep the area constant in any generalization level. Figure
2a
is depicting
shape area values course over generalization levels. It can be clearly seen that there
is an increase in the shape area of all four buildings. A steep increase is at the last
stages of generalization due to the generalization algorithm. There are also signif-
icant local peaks around simplification tolerance value of 30 m, 50 m (Lund
University) and 35 m (Houses of Parliament). Subsequently, the shape area
decreases, which is not desirable by means of polygon simplification for an output
map. Thus, one can identify levels of generalization that are not simplifying the
shape gradually, as expected.
Second easily calculable and interpretable metric is the shape length (Fig.
2b
).
On the contrary to the previous metric, shape length/perimeter should decrease as
the generalization continues. Again, the trend is confirming the assumption except
the last stages of generalization. Level of generalization at simplification tolerance
value of 200 m is too large and preserves undesirable details of ground plans. In the
case of the St. Maurice (Fig.
2g
) there is opposite trend (slight increase) from
simplification tolerance value of 25 m with the exception at values from 60 to
100 m.
Fractal dimension refers about overall complexity of the shape. It is supposed
that the higher level of generalization, the lower Fractal dimension value. In Fig.
2c
the assumption is confirmed. Except the tail of the graph, in the case of St. Maurice
and Houses of Parliament, where Fractal dimension value arose, therefore overall
complexity of these two shapes arose too (Fig.
2i
). In the last three levels (simpli-
fication tolerance values of 350, 400 and 500 m) all the ground plans
'
Fractal
dimension value was more or less the same and constant.
Following shape metrics are more difficult to interpret and are thoroughly
described by Parent (
2014
). Nevertheless, brief explanation is in Table
1
. Normal-
ized Detour index describes shape properties using convex hull, i.e. the convex
