Map Reconstruction Algorithm Based on Quadratic Optimization

Spatial data visualization is an important part of information visualization,and geographical map is the most common carrier of spatial data visualization.Generating simplified maps similar to traditional maps can improve the efficiency and accuracy of researchers and general public in analyzing and viewing spatial data.However,traditional process of reconstructing maps manually is tedious,and the reconstructed maps generated by existed algorithms are all composed of rectangular areas,which results in the loss of structural information.All of these factors may affect the visual perception of reconstructed maps.Our process of map reconstruction and visualization consists of following three steps,namely,reducing the amount of boundary data through data simplification,normalizing and removing boundary burrs through rectangularity and de-noise,and obtaining the optimal layout effect through quadratic optimization.In this paper,some provinces in China and regions of the United States except Hawaii and Alaska are selected as test sample.Compared with existed spatial ordered square layout algorithm,the proposed algorithm could better maintain the similarity between the reconstructed map and the original map with respect to the area shape and neighborhood relationship.