5 illustrates that the natural principle can be best depicted by
the operators developed in mathematical morphology and thus
the transformation in scale dimension can be best realised using
morphological techniques. In Section 6, some examples are
given, illustrating how morphological operators can be used for
transforming spatial representation from a larger scale to a
smaller scale.
2. A SCALE-DRIVEN FRAMEWORK
In order to understand the nature of generalization, it seems
necessary to compare digital generalization with traditional
manual generalization so that an insight into the matter may be
gained.
2.1 The factor directly driving generalization: Scale
To discuss the problems with digital generalization, it seems
pertinent to start with a discussion of the motivation behind
generalization. Many researchers have spent efforts on this
topic and identified some sets of requirements or controls have
as follows:
Müller (1991) considers that generalization is promoted by four
main requirements; i.e. economic requirements; data robustness
requirements; multipurpose requirements; and display and
communication requirements. Robinson et al (1995) has
identified another four elements (but called controls), i.e. map
purpose and condition of use; scale, graphic limits and quality
of data. Keates (1989) has also identified 4 elements, i.e. scale
and graphic requirements (legibility) and, characteristics and
importance. In a more detailed manner, McMaster and Shea
(1992) identified three sets of "philosophical objectives" as
follows: (a) Theoretical elements: reducing complexity;
maintaining spatial accuracy; maintaining attribute accuracy;
maintaining a logical hierarchy; and consistently applying
generalization rules; (b) Application-specific elements: map
purpose and intended audience; appropriateness of scale; and
retention of clarity and (c) Computational elements: cost
effective algorithms; maximum data reduction; and minimum
memory/disk requirement.
This is by no means an exhaustive list. It seems to the author
that some kind of "generalization" (or abstraction) needs to be
applied to these sets of motivation so that the problem can be
simplified and useful models established. This kind of
simplification is vital in scientific research. The classic
example of such a simplification is the Earth being simplified
by Newton as a point so that the Law of Gravitation could be
established.
To do this, some analysis needs to be carried out. Let's take
the "quality of data" as an example. The question arising is
“how does this factor affect generalization?” Suppose that a set
of data is for producing 1:10,000 scale map, if the quality of
the data is too poor to meet the accuracy requirement for this
scale, then one needs to map it at a smaller scale. Here comes
out the scale of map in between “data quality” (the reason) and
“generalization” (the consequence). Through applying a
similar analysis to other factors, it can be observed that scale is
the only factor directly driving the generalization process while
others can be considered as either indirect factors or posterior
factors. Indeed, the Swiss Society of Cartography has long ago
made it clear in its cartographic manual that generalization is
454
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
motivated only by a reduction of scale, as cited by Müller
(1991). Fig.1 shows such a relationship between various
motivations and the consequence.
Indirect Motivation Direct motivation Consequence
[Motivation 2 | Scale —} |Generalization
Fig.l Scale is the only direct motivation for generalization
2.2 A scale-driven framework
Now comes the question: “When can you consider
cartographic and other requirements?". To answer this
question, a discussion of the difference between traditional
manual generalization and digital generalization needs to be
conducted.
In manual generalization, both the simplification of the shape,
form and structure of map features and the consideration of
graphic legibility are considered simultaneously. This makes
the process appear to be very subjective. In fact, this
subjectivity is mainly caused by the consideration of the
“characteristics and importance” of features as pointed out by
Keates (1989). On the other hand, in a digital environment,
data resolution could be infinitely high, theoretically speaking.
For example, two lines with a spacing much less than 0.01 mm
is still separable in digital database. Therefore, graphic
legibility is not an issue for digital data itself. If the spatial data
is only for analytical analysis, no graphics needs to be
considered. Indeed, only when a graphic presentation is
considered, then comes the problem of graphic legibility,
resulting in exaggeration, displacement and other complex
operations. As a result of this reasoning, the relationship
between traditional and digital generalization can be expressed
by Fig.2.
Small Scale
Database
Digital-to-Digital >
Transformation
Digital-to-Graphic
Transformation Transformation
Large Scale
Database
Digital-to-Graphic |
Ÿ Ÿ
Large Scale > Manual > Small Scale
Graphic Map Generalization Graphic Map
Fig.2 Relationship between digital and manual map generalization
The digital-to-digital transformation is driven by scale. Such a
process will simplify the shape, form and structure of spatial
representation and should be very objective so that unique
solution can be achieved, given the same conditions. As will
be disc
conside
a natur:
It can t
the onl
Howev
accoun
require
that ce
digital-
to-digi
the car
digital
geogra
this sc
for ger
3
There
transfc
projeci
oriente
Howe
will b
transf«
(1994:
30. T
It has
reality
illustr
dimen
Fig.3.
(a)
(b) In
Just
syste!
repre
repre
syste
