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Ãû³Æ£ºEnergy Minimization Methods for Feature Displacement in Map Generalizaion ÄÉÃ×ÅÌÏÂÔØÁ´½Ó http://d.namipan.com/d/c099b4a6c ... 9104e02c0a03ffd5200 ÂÛÎĵÄÕªÒªÐÅÏ¢ 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 aecting 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 oers 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 modications 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 oer 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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