{"title":"Local Measures Distribution for the Estimation of the Elongation Ratio of the Typical Grain in Homogeneous Boolean Models","authors":"T. Eremina, J. Debayle, F. Gruy, J. Pinoli","doi":"10.5566/IAS.2554","DOIUrl":null,"url":null,"abstract":"We introduce a particular localization of the Minkowski functionals to characterize and discriminate different random spatial structures. The aim of this paper is to present a method estimating the typical grain elongation ratio in a homogeneous Boolean model. The use of this method is demonstrated on a range of Boolean models of rectangles featuring fixed and random elongation ratio. An optimization algorithm is performed to determine the elongation ratio which maximize the likelihood function of the probability density associated with the local perimeter measure. Therefore, the elongation ratio of the typical grain can be deduced.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"49 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Image Analysis & Stereology","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.5566/IAS.2554","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY","Score":null,"Total":0}
引用次数: 1
Abstract
We introduce a particular localization of the Minkowski functionals to characterize and discriminate different random spatial structures. The aim of this paper is to present a method estimating the typical grain elongation ratio in a homogeneous Boolean model. The use of this method is demonstrated on a range of Boolean models of rectangles featuring fixed and random elongation ratio. An optimization algorithm is performed to determine the elongation ratio which maximize the likelihood function of the probability density associated with the local perimeter measure. Therefore, the elongation ratio of the typical grain can be deduced.
期刊介绍：
Image Analysis and Stereology is the official journal of the International Society for Stereology & Image Analysis. It promotes the exchange of scientific, technical, organizational and other information on the quantitative analysis of data having a geometrical structure, including stereology, differential geometry, image analysis, image processing, mathematical morphology, stochastic geometry, statistics, pattern recognition, and related topics. The fields of application are not restricted and range from biomedicine, materials sciences and physics to geology and geography.
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