干旱区生态环境知识资源中心(Arid): Methods of computational topology and discrete Riemannian geometry for the analysis of arid territories

Arid

DOI	10.1080/23311916.2020.1808340
	Methods of computational topology and discrete Riemannian geometry for the analysis of arid territories
	Karimova, Lyailya; Terekhov, Alexey; Makarenko, Nikolai; Rybintsev, Andrey
通讯作者	Makarenko, N
来源期刊	COGENT ENGINEERING
ISSN	2331-1916
出版年	2020
卷号	7 期号:1
英文摘要	The purpose of this article is the development and application of discrete differential geometry methods for digital image analysis within the framework of Topological Data Analysis (TDA). The proposed approach consists of two stages. First of all, topological invariants, Betti numbers, are extracted from the digital image using TDA algorithms. They contain information about the appearance and disappearance of topological properties: the connected components and holes when filtering the image along with the height of the photometric topography. The interval of heights measuring the lifetime of a property is called the persistence of the property. The most common information about Betti's persistent numbers is presented in the form of a cloud of points on the birth-death diagram, the so-called persistence diagram (PD). The vectorization of PD with the help of a diffuse kernel makes it possible to estimate its pdf. At the second stage, we use the representation of the received pdf on the Riemannian sphere. Here, the Fischer-Rao metric reduces to the Hilbert scalar product of semi-density on the tangent bundle of a sphere. This approach allows you to analyze images of complex, multicomponent natural systems that do not have clear spectral boundaries of the transition between texture classes. Space images of natural landscapes were used as digital images. We demonstrate this technique to describe the morphological dynamics of wetlands located in arid zones and characterized by extremely high temporal variability.
英文关键词	TDA Betti numbers persistence fisher-rao information metric tangent bundle of Riemannian sphere remote sensing long-term dynamic
类型	Article
语种	英语
开放获取类型	DOAJ Gold
收录类别	ESCI
WOS记录号	WOS:000562158900001
WOS类目	Engineering, Multidisciplinary
WOS研究方向	Engineering
资源类型	期刊论文
条目标识符	http://119.78.100.177/qdio/handle/2XILL650/334552
作者单位	[Karimova, Lyailya; Terekhov, Alexey; Makarenko, Nikolai] Inst Informat & Computat Technol, Alma Ata B30C1Y3, Kazakhstan; [Makarenko, Nikolai; Rybintsev, Andrey] Russian Acad Sci Pulkovo, Cent Astron Observ, St Petersburg 196140, Russia
推荐引用方式 GB/T 7714	Karimova, Lyailya,Terekhov, Alexey,Makarenko, Nikolai,et al. Methods of computational topology and discrete Riemannian geometry for the analysis of arid territories[J],2020,7(1).
APA	Karimova, Lyailya,Terekhov, Alexey,Makarenko, Nikolai,&Rybintsev, Andrey.(2020).Methods of computational topology and discrete Riemannian geometry for the analysis of arid territories.COGENT ENGINEERING,7(1).
MLA	Karimova, Lyailya,et al."Methods of computational topology and discrete Riemannian geometry for the analysis of arid territories".COGENT ENGINEERING 7.1(2020).