Using an Energy Minimization Technique for Polygon Generalization |
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| Abstract: | Snakes are iterative energy-minimizing splines controlled by both internal constraint forces (internal energy) and external forces (external energy). This paper investigates the use of snakes for the resolution of conflicts in polygonal subdivisions (i.e., polygon maps or polygon mosaics) resulting from the violation of metric constraints which exist if a polygonal object is too small, too narrow, or too close to another polygon. Such metric conflicts are denoted as size and proximity conflicts. In the generalization of polygonal subdivisions, internal energy reflects the resistance of an object to deformation and external energy describes the need for generalization. This paper suggests the usage of a snakes-based algorithm which is triggered in such a way that it achieves the translation, a local and global increase (or decrease) of polygons, or an arbitrary combination of these transformations, depending on the conflicts encountered. Hence, size and proximity conflicts within a group of polygons can be solved simultaneously and holistically. Furthermore, snakes support the propagation of a change of a polygon's geometry to all adjacent neighbors. The proposed algorithm has been implemented in a prototype system that also supports a variety of other polygon generalization algorithms. The main difficulties identified are the intricate setup and fine-tuning of the snakes parameters and the computer resources required by the algorithm. However, the experiments showed that the proposed algorithm is a valuable method for the automated generalization of polygonal subdivisions. |
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