Research On Remote Sensing Image Segmentation Based On Persistent Homology And Ricci Curvature

Segmentation is the crucial step of remote sensing image interpretation and application.Traditionally,segmentation methods are based on spectral,spatial,texture,shape and statistical features of images usually expressed in the Euclidean space.Although these features expressed in the Euclidean space can provide rich cues to judge pixels belonging to the same(different)class(es),the features expressed on the Riemannian manifold can make full use of spectral,spatial and statistical information.Therefore,based on the Riemannian manifold,this paper further extracts image features by combining with cutting-edge mathematical tools such as persistent homology and Ricci curvature,and proposes more effective image segmentation algorithms.Around this scientific problem,the research content of this paper is summarized as follows.(1)The Riemannian manifold models of remote sensing image and its segmentation are constructed.For a given image,Gaussian Probability Distribution Function(GPDF)in an exponential family fashion is used to model the spectral measures of each pixel and its neighbor pixels.The Riemannian manifold,i.e.the data sub-manifold for the pixel,is built by taking the parameters of the GPDF exponential family model as its coordinates to depict the statistical characteristics of original image.By Legendre transformation,the data sub-manifold is transformed into a parameter sub-manifold to depict all possible segmentation results.Only points representing classes of current segmentation results are activated on the parameter sub-manifold.Finally,the segmentation is performed by projecting points of the data sub-manifold to the nearest activated point of the parameter sub-manifold,and updating all the activated points according to the projection results.As a result,all the activated points tend to be optimal segmentation.This image segmentation method is called manifold projection.The mathematical model is combining with persistent homology and Ricci curvature to improve the segmentation effect by both topology and geometry.(2)Segmentation algorithm by combining manifold projection and persistent homology.Firstly,the simplicial complexes are constructed from the original image,the topological relations among pixels are constructed and persistent homology is computed.Then,the optimal scale of simplicial complexes from persistent homology is calculated,and the corresponding homology group and connected regions are obtained.Homology group which is a topological object describing the whole pixel and connected regions which are some pixels belonging to the same class.The connected regions are used as features to improve the segmentation effect of manifold projection.(3)Segmentation algorithm by combining manifold projection and Ricci curvature.Based on the coordinates and spectral measures of points on the data sub-manifold,the Ricci curvature of two points is calculated.Two points with positive curvature are dense and belong to the same class,while two points with negative curvature are discrete and belong to the different classes.Ricci curvature are used as features to improve the segmentation effect of manifold projection.In order to qualitatively and quantitatively evaluate the segmentation effectiveness of the proposed algorithms,synthetic images,small scale real images and large scale real images are selected as the experimental scenes.It is evaluated by user’s accuracy,producer’s accuracy and overall accuracy,and compared with the classical image segmentation algorithms based on the features defined in the Euclidean space.Experimental results show that the segmentation effectiveness of the proposed algorithms is better than the classical image segmentation algorithms based on the features defined in the Euclidean space.It can be further proved that topology tools,like persistent homology and Ricci curvature,can contribute to the deep mining of image features and complete the segmentation task.The paper has 28 diagrams,9 tables and 74 references.