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Ãû³Æ£ºEnergy Minimization Methods for Feature Displacement in Map Generalizaion
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http://d.namipan.com/d/c099b4a6c ... 9104e02c0a03ffd5200
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The work reported in this thesis considers the issue of feature displacement in cartographic
generalization. Attempts to display cartographic data at scales smaller
than the source scale result in spatial con
icts; map symbols clutter or overlap.
Several map generalization operators may be applied to resolve these problems,
including displacement. The main goal of displacement is to separate con
icting
objects, either by deformation of their outline or by shifting them in their entirety.
Cartographic displacement is a contextual operation, dealing with several objects
at once, and also a ecting the neighborhood of the con
icting features. Local
reasoning often fails, since con
icts are not solved, but simply pushed back and
forth. Existing sequential displacement algorithms fail to incorporate the required
broader view necessary for successful generalization.
This thesis proposes new techniques to handle displacement. Instead of working
through all proximity con
icts one after the other, as executed by sequential methods,
a global approach is adopted. Here, cartographic displacement is interpreted
as an optimization problem. The proposed models thereby rely on an interplay of
external and internal forces which compete a solution. Internal regularizing forces
constrain the displacement of map objects or object structures, while at the same
time proximity con
icts give rise to external forces, which try to deform objects
and push them away from con
icts. A balance between internal and external forces
is iteratively sought { the system energy is minimized.
For the modeling of regularizing structures, this research draws upon techniques
used in engineering sciences. In the thesis, care is taken to illustrate the background
and theory of these techniques for geographers who are perhaps less familiar with
this subject. A goal of this study is to adapt these techniques to demands arising
in cartography. The success of the new algorithms depends on the way in which
cartographic constraints and cartographic knowledge can be translated into the
numerical methods.
Three algorithms are proposed. First, the use of snakes { a widespread technique
in computer vision { is investigated for the cartographic displacement of
roads. This technique o ers a promising way to constrain road shapes and to reach
a good displacement solution iteratively. It is described how snakes can be set up to
allow the cushioning of displacement through line networks, which frees roads from
the rigid restriction of xed junction nodes. Further, the importance of junctions
is pointed out for the displacement operation. It is shown how formerly computed
local modi cations of the junction geometry can be incorporated into the iterative
process.
A second algorithm for road displacement makes use of elastic beams, a concept
originally developed in structural mechanics. Beams prove to be better suited for
road displacement than snakes, since they provide a control of road directions and
o er an interface over which a cartographic behavior can be carried over on the
roads; bending and stretching of road segments can be controlled explicitly.
Finally, the work addresses building displacement in urban blocks. Even though
the constraints guiding this class of displacement vary from the ones handled in
road displacement, a tool from structural mechanics again provides useful input.
The structure of buildings is interpreted as ductile truss, wherein characteristic
object relations can be controlled and preserved.
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