Surface Feature Extraction And Topology Simplification Based On Piecewise Linear Morse Theory

The extraction of terrain surface topological features is an important part of geographic information research,and it is of great significance to many fields such as surface modeling,cartography,and terrain analysis.There are various changes in the terrain surface undulations.From the perspective of terrain surface characteristics,it is difficult to find a unified index for terrain surface description,but from the topological perspective,the composition of the terrain surface morphology has a pattern to follow,and the surface morphology can be described by specific terrain surface topological characteristics.And the ridge lines and valley lines are formed by peak points,valley points,and saddle points are important features that describe the terrain surface morphology.A complete feature line can build a good data foundation for subsequent data processing and analysis.3D laser scanning technology is an important tool for terrain surface data acquisition,which can quickly obtain relatively complete terrain surface point cloud data,but there are some problems such as huge data volume,data information redundancy,and no topological structure.Therefore,how to identify terrain surface feature points and complete the construction the feature line generates a good terrain surface topological structure,which is the main research content of terrain surface feature extraction and topology simplification.Aiming at the deficiencies of terrain surface point cloud data and the inaccurate feature recognition of traditional terrain surface feature extraction algorithms,incomplete topology construction,and poor adaptability of feature importance metrics,firstly preprocesses the terrain surface point cloud data,and then focuses on scientific issues such as terrain surface feature recognition and construction,feature importance measurement and feature topology simplification under the piecewise linear Morse theory.The main research contents are as follows:(1)The filtering algorithm and systematically introduction of the Morse theory are summarizedThe point cloud filtering algorithm is introduced in detail,focuses on the birth,principle and application of the piecewise linear Morse theory.On the one hand,the commonly used point cloud filtering algorithms are introduced in detail,and the shortcomings of the algorithms are summarized.On the other hand,a good topological structure for terrain surface point cloud data can be constructed by piecewise linear Morse theory,which realizes terrain surface feature extraction and topology simplification.The development,principle and application of classical Morse theory,discrete Morse theory,and piecewise linear Morse theory are elaborated.And the related concepts of Morse theory,such as topology,Hessian matrix,critical points,Morse-Smale complex and so on are systematically introduced.(2)An adaptive threshold point cloud filtering algorithm is improvedAiming at the problems of poor adaptability and too many artificial factors in the commonly used point cloud filtering algorithms,an adaptive threshold point cloud filtering algorithm is improved which based on the moving surface.The adaptive filtering threshold is set by the curvature limit value.Firstly,the hybrid least squares method is used to fit the surface more accurately.Then the difference between the elevation value of the fitted surface and the real ground elevation is used to calculate and set the first-level filtering threshold to filter out the larger-sized features.Finally,the real ground elevation value of the lowest point of the grid is used to calculate the curvature limit value,and the secondary filter threshold is set to filter out non-ground points which are similar to the ground.Experimental results show that the average total error of the algorithm's filtering reaches 6.26%,and the total error of continuous terrain filtering can reach below 4.00%,which means it can distinguish ground points from non-ground points more accurately,with high accuracy and strong adaptability.(3)The terrain surface feature extraction and topology construction under the piecewise linear Morse theory are realizedAiming at the problems of low accuracy of traditional terrain surface feature extraction algorithms and incomplete topology construction of commonly used surface data structures,feature extraction and topology construction of terrain surface point cloud data are achieved by piecewise linear Morse theory in this paper.Firstly,the critical points(peaks,pits and saddles)are classified and extracted by calculation of the critical value of the piecewise linear Morse function.Then,according to a certain pathfinding path,a characteristic line is constructed to generate a Morse-Smale complex to divide the entire surface into a four-sided grid,and the ridge and valley lines are extracted to establish a good topological structure for the surface point cloud data.The experimental results show that the average point cloud compression rate of the feature extraction of the algorithm reaches 22.82%,which can build a complete topological structure of the terrain surface as a whole,and extract the main feature lines to express the topological features of the surface.(4)A new feature importance measurement index is proposed to achieve topology simplificationAiming at the problem of poor adaptability of traditional feature importance metrics,a new feature importance metrics is proposed based on the theory of "Persistence".Firstly,the classic persistence value of the feature point is calculated as a feature importance indicator to evaluate the feature importance of Morse-Smale.Then the importance of the feature points is evaluated again by the feature importance index of the Morse-Smale complex,and a new feature importance metric is formed after calculation,which measures the feature importance of the Morse-Smale complex again to complete the topology simplification.Experimental results show that the feature importance index is further refined,and the redundant terrain surface features is eliminated so that a precise and concise topology is built.The average point cloud compression rate reaches 70.82%,which greatly reduces the amount of data while ensuring the accuracy of topology simplification.And a good data foundation for the subsequent processing and analysis of terrain data is laid.