Algebraic Multi-Layer Network: Key Concepts

作     者：Khanykov, Igor Nenashev, Vadim Kharinov, Mikhail 

作者机构：Russian Acad Sci St Petersburg Fed Res Ctr Lab Big Data Technol Sociocyberphys Syst 14 Line VO 39 St Petersburg 199178 Russia St Petersburg State Univ Aerosp Instrumentat Inst Comp Syst & Programming Lab Intelligent Technol & Modelling Complex Syst 67 B Morskaia St St Petersburg 190000 Russia 

出 版 物：《JOURNAL OF IMAGING》 (J. Imaging)

年 卷 期：2023年第9卷第7期

页      面：146-146页

核心收录：

基　　金：Russian Science Foundation [FFZF-2022-0006] 22-79-00303 

主　　题：image processing cluster analysis of big data Ward's pixel clustering Sleator-Tarjan dynamic trees 

摘      要：The paper refers to interdisciplinary research in the areas of hierarchical cluster analysis of big data and ordering of primary data to detect objects in a color or in a grayscale image. To perform this on a limited domain of multidimensional data, an NP-hard problem of calculation of close to optimal piecewise constant data approximations with the smallest possible standard deviations or total squared errors (approximation errors) is solved. The solution is achieved by revisiting, modernizing, and combining classical Ward s clustering, split/merge, and K-means methods. The concepts of objects, images, and their elements (superpixels) are formalized as structures that are distinguishable from each other. The results of structuring and ordering the image data are presented to the user in two ways, as tabulated approximations of the image showing the available object hierarchies. For not only theoretical reasoning, but also for practical implementation, reversible calculations with pixel sets are performed easily, as with individual pixels in terms of Sleator-Tarjan Dynamic trees and cyclic graphs forming an Algebraic Multi-Layer Network (AMN). The detailing of the latter significantly distinguishes this paper from our prior works. The establishment of the invariance of detected objects with respect to changing the context of the image and its transformation into grayscale is also new.