Quick computation program of fractal dimension for 2D vector data

• Published in: 2009 17th International Conference on Geoinformatics pp. 1 - 4
• Main Authors: Qian Wang, Quanfang Wang, Xin Mei, Haiwen Zhang, Hangzhou Sun
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-08-2009
• Subjects: Accuracy; fractal dimension; Fractals; Geography; Geometry; Image converters; Least squares methods; Pixel; programming; Software maintenance; Solid modeling; vector data; visual c#
• ISBN: 1424445620; 9781424445622
• ISSN: 2161-024X
• DOI: 10.1109/GEOINFORMATICS.2009.5292827

Fractal dimension plays an important role in representing fractal feature of instable, irregular, highly complex and self-similarity geometric objects, which are often seen in nature but couldn't be effectively described by using traditional models based on Euclid geometry. Now the fractal dimension is usually calculated on raster data, but in fact, quite a number of spatial data is stored as vector data, which has great capability in true description of spatial structure information of geographic entity in real world. If these vector data are converted to images to calculate fractal dimension, perhaps some pixels with inaccurate grey value will result from the ldquoGRIDrdquo structure of raster data and accordingly reduce the accuracy of calculation. What is more, the precision calculated on Raster Data is closely related to the size of pixel and Grid image. In this paper, a quick computation program of the fractal dimension for 2D vector data based on Windows platform has been designed by using Visual Csharp. The main process of disposing is to read area and perimeter data of polygons and build regression models, then the fractal dimension is calculated on Least Square Method. Validation of the program has been successfully done by adopting existing landscape data supplied in a book named Mathematical Methods in Contemporary Geography. Moreover, the program has been applied to calculate the fractal dimension of land-use types in Qinling Mountains and the southeast Hubei Province, China. The results show that the following advantages of this program have been found: higher calculating precision; superior to SPSS software and Microsoft Office Excel at calculation speed, which is particularly prominent when applied to a batch vector data processed; easily operated, expanded and maintained; easily attaching the calculating results to the attribute table of raw 2D vector data and auto-arrange ascendingly or descendingly the fractal dimension value, which could consumedly improve working efficiency; and able to show the fractal dimension of per polygon by thematic map, which will be useful to study spatial distribution characteristics of geometric objects.