Fig.12 is another example which shows the transformation of
the representation of area features in scale dimension.
Si Y "
(a) Original feature (b) Result of 10x reduction (c) final result
Fig.12 Another example of area aggregation (Su et al, 1996)
7. CONCLUDING REMARKS
Digital generalization of spatial data can be decomposed into
two processes, ie. a digital-to-digital transformation and a
digital-to-graphic transformation. The latter is about
cartographic presentation, thus cartographic knowledge can be
formalised and knowledge-based systems used at this stage.
Some of multi-purpose requirements might be also be applied
here.
The digital-to-digital transformation is a transformation in scale
dimension and thus the process itself should be objective. It
has been argued in this paper that the transformation in scale
dimension is guided by a natural principle (Li and Openshaw,
1993) and this natural principle can be best depicted by the
operators developed in mathematical morphology, which is a
science dealing with shape, form and structure of objects. It
means that, upon the two basic operators -- i.e. dilation and
erosion -- in mathematical morphology, some basic
mathematical models for transforming spatial representation in
scale dimension can be built. These models, like affine,
projective, conformal transformation efc in space dimension,
will be of fundamental importance to generalization. If and
only if these basic transformation models are developed, will
one be able to develop a system which will be capable of
producing consistent results.
Indeed, the development of such basic mathematical models for
transformation in scale dimension based on morphological
operators has been carried out by the author and his
collaborators since the first study by the author (Li, 1994b) and
some promising results have also been obtained (Li and Su,
1995; Su and Li, 1995; Su et al, 1996).
It is a commonplace that there are many routes available for
travelling from Hong Kong to Vienna although some are with
longer distance while others may have shorter distance. But
there is only one unique shortest distance between these two
cities, i.e. the geodetic line. In practice, this line may be either
difficult to determine or difficult to travel along. This paper is
yet another attempt to find a feasible route for digital
generalization in GIS environment but certainly this route is
still not the geodetic line of digital generalization. Indeed, it is
the author's hope that this paper will somehow contribute to
the discovery of this geodetic line.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
ACKNOWLEDGMENTS
The author would like to thank Mr. B. Su for producing
diagrams used in Fig.6 and Fig.7 of this paper.
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