Fractal Dimension Calculation Of Complex Terrain Based On The Inverse Box Counting Algorithm

A variety of geomorphic types,such as mountains,hills,basins and gullies,are formed by various factors(such as rainfall,wind,geological structure and artificial tillage)on the surface of the terrain,and they have their own unique fractal characteristics.However,these complex landforms can not be accurately described by using Euclidean geometry method.With the development of fractal theory,the research of fractal in the field of geoscience has gradually enriched,and it provides a new way of thinking for the analysis and extraction of geomorphic spatial characteristics.Fractal theory and fractal methods naturally become powerful tools for dealing with this complexity,especially for geomorphic systems involving spatial phenomena.DEM and point cloud data are the main data forms for describing landforms and landforms.At present,there are many researches on fractal dimension of DEM,whilst the research on fractal dimension calculation of point cloud data is still not enough.Therefore,a special fractal analysis system software is designed and developed to study the calculation method,the influence factors and spatial differentiation characteristics from the DEM and point cloud data of 30 samples in Bengbu(plain)and Xi'an(mountainous and mixed terrain).At the same time,a method of calculating and analyzing the fractal dimension of DEM and point cloud data using the inverse Box Counting Algorithm is explored.First of all,by analyzing the fractal dimension of the terrain surface of DEM data,a Box Counting Algorithm was designed to calculate the fractal dimension of the curve.The Box Counting Algorithm,used as a measure of irregularity and roughness of fractals with self-similarity property,requires a proper choice of the number of box sizes,corresponding sizes,and size limits to guarantee the accuracy of the fractal dimension estimation.The Box counting is a method of gathering data for analyzing complex patterns by breaking an image into smaller and smaller pieces,typically "box"-shaped curve and analyzing the pieces at each smaller scale.This method of processing images will increase a lot of work.The program actually gets the pixel matrix of the image,and sometimes can not be subdivided into smaller units.For this reason,a way of reverse thinking is proposed by merging pixel points to a larger squares.When the fractal curve is sufficiently close to the "box"-shaped curve,the proportion of the square that passes through the curve is the fractal dimension.Then,the same principle is used to calculate the data point cloud.Unlike image data,the point cloud data is a pixel matrix,which can be processed by upgrading the grid dimension of Row and Column,and distinct processing of Row,Column and Z data to ensure the contour line be not recoincide;and the process is repeated using a larger square dimension.When the fractal curve is sufficiently close to the curve,the proportion of the square that passes through a curve is the fractal dimension.Finally,by defining the data sampling window,the average height and the standard deviation height of the point cloud data are calculated.And the fractal dimension and fractal feature of the DEM and point cloud data were analyzed.and the changing rules between the fractal dimension and the geoscience index are analyzed.(1)The inverse Box Counting Algorithm can deal with DEM and point cloud data well and calculate fractal dimension.The system software has good universality.(2)The influence parameters of fractal dimension value was calculated.The DEM image is obtained by interpolating the fitting curve of the point cloud data,and then be rendered using stratified rendering method.In fractal dimension calculating process,the DEM image is directly withdrowned from combination of pixels,while the point cloud data is controlled by the data merging of different contour lines.So the fractal dimension value of the DEM fractal dimension is larger than what the point cloud data does.(3)By comparing the data of fractal dimension and geoscience index,there is no necessary relationship between the change of fractal dimension and the average height,and the change trend of the fractal dimension and the standard difference height is inversely proportional.