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A proof of image euler number formula

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Science in China(Series F) 2006年第3期49卷 364-371页

作者： LIN Xiaozhu SHA Yun JI Junwei WANG Yanmin Information Engineering School Beijing Institute of Petrochemical Technology Beijing 102617 China

euler number is one of the most important characteristics in topology. In twodimension digital images, the euler characteristic is locally computable. The form of euler number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor number, a formula of the euler number computing is proposed and is proved in this paper. It is a new idea to locally compute euler number of 2D image.

关键词： topology euler number binary image 4-connected 8-connected.

Fast Object Extraction and euler number on Block Represented Images

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Journal of Data Analysis and Information Processing 2022年第2期10卷 91-109页

作者： Iraklis M. Spiliotis Alexandros S. Peppas Nikolaos D. Karampasis Yiannis S. Boutalis Department of Electrical and Computer Engineering Democritus University of Thrace GR Xanthi Greece

The identification of objects in binary images is a fundamental task in image analysis and pattern recognition tasks. The euler number of a binary image is an important topological measure which is used as a feature in image analysis. In this paper, a very fast algorithm for the detection and localization of the objects and the computation of the euler number of a binary image is proposed. The proposed algorithm operates in one scan of the image and is based on the Image Block Representation (IBR) scheme. The proposed algorithm is more efficient than conventional pixel based algorithms in terms of execution speed and representation of the extracted information.

关键词： Image Block Representation Object Detection Hole Detection euler number Connected Components Labeling

The History of the Derivation of euler’s number

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Journal of Applied Mathematics and Physics 2022年第9期10卷 2780-2795页

作者： Mohsen Aghaeiboorkheili John Giuna Kawagle Department of Mathematics and Computer Science University of Technology Lae Papua New Guinea Department of Civil Engineering University of Technology Lae Papua New Guinea

This paper summarizes the works of numerous inspiring hard-working mathematicians in chronological order who have toiled the fields of mathematics to bring forward the harvest of eulers number, also known as Napiers n... 详细信息

关键词： euler number Napier number History of Mathematics

Retrieving Topological Information of Implicitly Represented Diffuse Interfaces with Adaptive Finite Element Discretization

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Communications in Computational Physics 2013年第5期13卷 1209-1226页

作者： Jian Zhang Qiang Du Supercomputing center Chinese Academy of SciencesBeijingP.R.China Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA State Key Laboratory of Space Weather Chinese Academy of SciencesBeijingP.R.China

We consider the finite element based computation of topological quantities of implicitly represented surfaces within a diffuse interface *** an adaptive finite element implementation with effective gradient recovery techniques,we discuss how the euler number can be accurately computed directly from the numerically solved phase field functions or order *** examples and applications to the topological analysis of point clouds are also presented.

关键词： Diffuse interface model phase field method euler number Gauss curvature adaptive finite element gradient recovery

Differential Structure of Certain C(X)×αZ

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Acta Mathematica Sinica,English Series 1995年第3期11卷 225-231页

作者： Lin Qing Institute of Mathematics Academia Sinica Beijing

In this paper, we show that, without involving the C~*-bundle theory, elementary differ- ential topology can do the classification of homogeneous C~*-crossed product C(X)×α Z, where X is a compact differentiable manifold of low dimension and α is a diffeomorphism of X. The motivation of this work is the Shultz’s theorem which states that a C~*-algebra can be identified with its pure state space carrying w~*-topology and certain geometric structure.

关键词： C~*-crossed product Pure state Fibre space euler number Rational rotation algebras

SIMPLE QUALITY ASSESSMENT FOR BINARY IMAGES

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Journal of Electronics(China) 2007年第2期24卷 204-208页

作者： Zhang Chun＇e Qiu Zhengding Institute of Information Science Beijing Jiaotong University Beijing 100044 China

Usually image assessment methods could be classified into two categories: subjective as-sessments and objective ones. The latter are judged by the correlation coefficient with subjective quality measurement MOS (Mean Opinion Score). This paper presents an objective quality assessment algorithm special for binary images. In the algorithm, noise energy is measured by Euclidean distance between noises and signals and the structural effects caused by noise are described by euler number change. The assessment on image quality is calculated quantitatively in terms of PSNR (Peak Signal to Noise Ratio). Our experiments show that the results of the algorithm are highly correlative with subjective MOS and the algorithm is more simple and computational saving than traditional objective assessment methods.

关键词： Image quality assessment Euclidean distance euler number

Some Properties of a Class of Refined eulerian Polynomials

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Journal of Mathematical Research with Applications 2019年第6期39卷 593-602页

作者： Yidong SUN Liting ZHAI School of Science Dalian Maritime University

Recently, Sun defined a new kind of refined eulerian polynomials, namely,■for n ≥ 1, where Sn is the set of all permutations on {1, 2,..., n}, odes（π） and edes（π） enumerate the number of descents of permutation π in odd and even positions, respectively. In this paper,we obtain an exponential generating function for A_n（p, q） and give an explicit formula for A_n（p, q）in terms of eulerian polynomials A_n（q） and C（q）, the generating function for Catalan *** certain cases, we establish a connection between A_n（p, q） and A_n（p, 0） or A_n（0, q）, and express the coefficients of A_n（0, q） by eulerian numbers An,k. Consequently, this connection discovers a new relation between euler numbersEn and eulerian numbers An,k.

关键词： eulerian polynomial eulerian number euler number descent alternating permutation Catalan number

Entropy and topology of the Kerr—de Sitter black hole

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Chinese Physics B 2002年第1期11卷 87-90页

作者：陈松柏荆继良 InstituteofPhysicsandDepartmentofPhysics HunanNormalUniversityChangsha410081China

By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole isinvestigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of theeuler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin ofthe entropy of the black hole is related to the topology of its instanton.

关键词： entropy of black hole constrained gravitational instanton euler number