Study on Evaluation Index System of Contour Simplification Algorithms
There are many algorithms available for automatically simplifying contours on map during the process of map generalization. These algorithms can dramatically reduce the number of vertex of a contour resulting in effective spatial data compression and efficiency of data rendering. According to the principle of choosing vertex of a polyline and setting search areas, these methods can be divided into five categories: Independent Point Routines, Local Processing Routines, Unconstrained Extended Local Processing Routines, Constrained Extended Local Processing Routines, and Global Routines. All the kinds of polyline simplification algorithms will affect the quality of contour data in different ways. Here the quality of contour data may refer to positional accuracy, shape/size precision, and attribute accuracy etc. Errors generated from simplification process will vary by using different algorithms or different compression ratio achieved. With deepening research in contour simplification algorithms, it is increasingly important to study the evaluation methods of the simplified results.
The prevailing quality evaluation method of spatial data simplification is to analyze the changes in geometry and topology. But this evaluation method only regards contours as ordinary polylines, neglecting the geographic characteristics of a contour as a carrier of landform information. Consequently the current evaluation methods only use simple comparative and qualitative analysis.
This paper aims to establish a universal error evaluation index system for contour simplification algorithms concerning both geometric errors and attribute data errors. The evaluation of geometric errors including length error, displacement error, buffer tolerance and topology error, whereas the evaluation of geographical attribute errors can be measured by constructing DEMs first, and then performing statistical analyses.
This study takes a hypsographic map of Biyun?an in the region of Lushan, Jiangxi province, China as the experimental data, and simplifies contours using 11 well-known simplification algorithms carry out by the programming language of C++. Then systematically evaluated the errors of these algorithms. The 11 algorithms are Nth Point, Randomly Select, Distance between Points, Perpendicular Distance, Angular change between points, Jenks algorithm, Visvalingam-Whyatt algorithm, Reumann-Witkam algorithm, Opheim algorithm, Lang algorithm, and Douglas-peucker algorithm.
Study shows the evaluation index system can take a global analysis of contour simplification errors by considering both aspect of geometry and geography. The results are useful for choosing alternative algorithms in case of different circumstances.
Keywords: Cartography, Generalization, Simplification, Algorithms, Programming, Automation, Error, Geometric