Multi-scale Spatial Similarity Relations Measurements For Automatic Contour Generalization

Spatial relation refers to the relations between entities or phenomena in geographical space caused by spatial location,including distance,direction,topological,similarity and correlation relation.As an important part of spatial relation,spatial similarity relation,including graph similarity,topological similarity,semantic similarity,and scene similarity,has been widely used in spatial cognition,and intelligent processing of spatial data,such as spatial query,spatial data matching,and pattern recognition,especially automatic map generalization.Contour,as an effective means for representing 3-dimensional topographic features on2-dimensional surfaces,has been widely used in cartography and geographical information engineering.And contour automatic generalization is essential for the reduction of small scale topographic maps,the topographic analysis based on terrain and the construction of multi-scale vector topographic map database.However,automatic contour generalization,including map generalization algorithm,process control of map generalization,and evaluation of map generalization results,has not been fully realized.Map generalization essentially is a kind of spatial similarity transformation between multi-scale maps.However,there is still a lack of automatic map generalization system based on spatial similarity relation theory,and spatial similarity relation of multi-scale contour cluster also is seldom researched.From the perspective of spatial cognition,when reading a map,it is usually done in a gradual progression from coarse to refined,from whole to field to individual;and according to Gestalt psychology.For a contour map,people often first pay attention to the overall geomorphic distribution of the whole map,the pay attention to the adjacent distribution information of adjacent contour line pairs,and finally pay attention to the more detailed information of a single contour line.Therefore,Based on the multi-scale vector contour cluster of 1:5000,1:10000,1:50000,1:100000,and 1:250000 of different geomorphic types were used as experimental datasets,this paper firstly studied the spatial similarity between individual contour lines oriented to automatic simplification of polyline,and then spatial similarity relation of multi-scale contour cluster is researched deeply,including the quantitative expression methods of spatial similarity relations and the quantitation function relation between spatial similarity degree of multi-scale contour clusters and map scale change.The main works and innovations of this paper include the following three aspects:(1)This paper proposes to take the spatial similarity evaluation model of multi-scale contour line as the coincidence point,and determines the quantitative relationship between them using the principle of threshold parameter optimization to realize the automation simplification of polyline based on DP algorithm,.The results indicate that exponential function is the best to express the quantitative relationship between multi-scale spatial similarity degrees of contour line and map scale change,and quadratic function is the optimal functions to describe the quantitative relationship between the optimal distance threshold and map scale change.And simplification results of the proposed method in this paper are in well match with the existing target scale data,which effectively avoids the subjective dependence of cartographer in the process of polyline simplification,and improve the simplification efficiency and the accuracy of simplification results.It also provides a method system and support for the fully automatic polyline simplification.(2)This paper developed a quantitative expression of topological relations of contour cluster based on directed contour tree,which makes up for the shortcomings of traditional topological relation quantitative expression method based on undirected contour tree,such as incomplete,repeated accumulation between topological types and missing calculation.After this,108 groups of multi-scale contour clusters with different geomorphological types were employed to explore the changing regularity of topological indices with map scale.The results show that the quantitative expression of multi-scale topological indexes is closely related to the contour interval change;power function is the best fit among the candidate functions.This conclusion is of great significance to the improvement of spatial cognition of multi-scale contour topological relations,and further demonstrates that it is reasonable and possibility for contour cluster to realize the automatic generalization based on multi-scale spatial similarity relations.(3)The paper constructed a indirectly measurement method of multi-scale contour cluster morphological similarity,which make up for the gap of existing research on morphological similarity measurement methods of multi-scale contours.After this,13 groups of multi-scale contour clusters of the Loess geomorphy were employed to explore the quantitative changing regularity of multi-scale morphological similarity degree with map scale change.The result show that power function also is the best to fit the quantitative function relationship between multi-scale morphological similarity degree and map scale change of contours from the Loess geomorphy.This conclusion further indicates that it is possibility for contour cluster to realize the automatic generalization based on multi-scale spatial similarity relations,and provides theoretical methodological basis for spatial cognition improvement and intelligent processing of spatial data,such as morphological recognition,and spatial data matching,etc.In this paper,the measurement methods of topological similarity and morphological similarity between multi-scale contour clusters is proposed from three dimensions,which includes macroscopic morphological and morphological similarity of overall geomorphology,spatial relation similarity between adjacent contour line,and spatial similarity between contour line.And the quantitative relationship between multi-scale between multi-scale contour spatial similarity and map scale change.Compared with traditional researches on spatial similarity of contour based on geometric features,this paper not only considers the cluster of contour line,but also considers the importance of spatial relation and structure description of contours in the process of contour generalization.Research results indicate that power function is the best to express the quantitative relationship between multi-scale contour topological and morphological similarity degree and map scale change.The quantitative relationship between them of multi-scale contour with the same geomorphic type can be expressed using the same power function.This conclusion further demonstrates that it is rationality and possibility for the realization of automatic contour generalization based on multi-scale spatial similarity relation,and it provides theoretical and technical support for intelligent processing of spatial data,such as spatial cognition and reasoning,multi-scale spatial data query,matching and morphological recognition,especially the construction of contour vector topographic map database.