Research On Sampling Density In Feature-based DEM Generalization

As a fundamental issue in geo-sciences,the effects of scale in data and data processing are well recognized as“one of the most fundamental aspects of any research”.Both the terrain parameters and the features are inevitably dependent upon the scale of applications.This is reflected in the existence of correlations and differences between terrain parameters and features of coarser topography and finer topography of the same region.To analyze and study this correlation and difference,it is necessary to establish Multi-scale terrain,which is called terrain generalization.Terrain generalization often uses feature-based methods for simplification.This method first extracts terrain features from the original DEM based on the specific algorithm.Construct a triangulation irregular network for the terrain features obtained,and then generate a regular grid DEM at the target scale by interpolating TIN.Due to the particularity of the TIN structure,the scale information contained therein cannot be quantitatively expressed.Therefore,the problem of determining the target resolution needs to be considered in the process of converting the TIN to the regular grid DEM.This problem can be further translated into the fact which scale of terrain that a certain number of topographic features extracted from the original terrain can express.Based on the above problems,this paper studies the sampling density problems involved in feature-based terrain simplification methods.Using terrain average slope as an indicator to describe the complexity of the terrain,a series of terrains with different terrain morphology were selected.Using the maximum Z tolerance method and the skeleton line constraint method to generalization the original DEM,a simplified terrain with different coarse resolutions was generated.Using the accuracy of generalized DEM as the criteria,the effects of terrain morphology,simplification methods,and target scale on sampling density were analyzed.The feature-based simplification method is compared with the uniform sampling method in an accuracy-equivalent manner.Using the accuracy equivalence method and the 1.1 times of the limit accuracy of the coarser DEM,the simplified terrain sampling densities for different target scales of different terrain simplification methods are determined.The experimental results show that:?1?With different terrains and different target scales,as the sampling density gradually increases,the simplified terrain elevation accuracy rapidly increases and gradually tends to the coarser DEM accuracy.Simplification of terrain elevation accuracy is limited by the target resolution.The maximum accuracy that can be achieved by simplifying terrain at different target scales is different.The rougher the target scale,the lower the highest accuracy that can be achieved by simplifying the terrain;?2?The limit accuracy of the simplified terrain decreases linearly with the increase of the average slope of the terrain.?3?Compared with the simplified terrain scale,the average slope of the terrain has little influence on the sampling density.The sampling density reduced to a certain target scale fluctuates roughly within a certain range.When the average slope is small,the sampling density is higher than other areas.This paper obtains the relationship between the target scale and the sampling density under the extreme accuracy of the simplified terrain when the topographic average slope is greater than 2°and the terrain is simplified using the maximum Z tolerance method and the skeleton line constraint method.The relationship between the target scale and sampling density obtained by simplifying using the Z tolerance method is:y_z=2594.4x_z^-1.298?R²=0.9873?.The relationship between the target scale and sampling density obtained by simplifying using the skeleton line constraint method is:y_g=23214x_g^-1.623?R²=0.9999?.Where x is the resolution of the simplified DEM?in m?and y is the sampling rate?number of sampling points/the original DEM total number of grids 100?.