{"title":"Unique Reconstruction of a Lambertian Optical Surface from Images","authors":"E. Yu. Derevtsov","doi":"10.1134/s1055134424030036","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Within the framework of inverse problems of photometry, we study questions on\nreconstruction of the spatial location and luminosity of a Lambertian optical surface from its\nimages obtained with the use of a small number of optical systems. We study causes of ambiguity\nin reconstruction of the location of such a surface. We suggest criteria for existence of a unique\nsolution of the inverse problem on reconstruction of a luminous surface from three images for\ngeneral weight functions and apply the results to specific classes of weight functions that model\nthe degree of transparency of the medium (including its absorption or scattering).\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424030036","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Within the framework of inverse problems of photometry, we study questions on
reconstruction of the spatial location and luminosity of a Lambertian optical surface from its
images obtained with the use of a small number of optical systems. We study causes of ambiguity
in reconstruction of the location of such a surface. We suggest criteria for existence of a unique
solution of the inverse problem on reconstruction of a luminous surface from three images for
general weight functions and apply the results to specific classes of weight functions that model
the degree of transparency of the medium (including its absorption or scattering).
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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