{"title":"面心立方网格上拓扑保全并行还原的充分条件","authors":"Gábor Karai, Péter Kardos, Kálmán Palágyi","doi":"10.1007/s10851-024-01177-y","DOIUrl":null,"url":null,"abstract":"<p>Topology preservation is a crucial issue in parallel reductions that transform binary pictures by changing only a set of black points to white at a time. In this paper, we present sufficient conditions for topology-preserving parallel reductions on the three types of pictures of the unconventional 3D face-centered cubic (FCC) grid. Some conditions provide methods of verifying that a given parallel reduction always preserves the topology, and the remaining ones directly provide deletion rules of topology-preserving parallel reductions, and make us possible to generate topologically correct thinning algorithms. We give local characterizations of P-simple points, whose simultaneous deletion preserves the topology, and the relationships among the existing universal sufficient conditions for arbitrary types of binary pictures and our new FCC-specific results are also established.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sufficient Conditions for Topology-Preserving Parallel Reductions on the Face-Centered Cubic Grid\",\"authors\":\"Gábor Karai, Péter Kardos, Kálmán Palágyi\",\"doi\":\"10.1007/s10851-024-01177-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Topology preservation is a crucial issue in parallel reductions that transform binary pictures by changing only a set of black points to white at a time. In this paper, we present sufficient conditions for topology-preserving parallel reductions on the three types of pictures of the unconventional 3D face-centered cubic (FCC) grid. Some conditions provide methods of verifying that a given parallel reduction always preserves the topology, and the remaining ones directly provide deletion rules of topology-preserving parallel reductions, and make us possible to generate topologically correct thinning algorithms. We give local characterizations of P-simple points, whose simultaneous deletion preserves the topology, and the relationships among the existing universal sufficient conditions for arbitrary types of binary pictures and our new FCC-specific results are also established.</p>\",\"PeriodicalId\":16196,\"journal\":{\"name\":\"Journal of Mathematical Imaging and Vision\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Imaging and Vision\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10851-024-01177-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Imaging and Vision","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10851-024-01177-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
摘要
在通过一次只将一组黑点变为白点来变换二值图片的并行还原中,拓扑结构的保持是一个关键问题。在本文中,我们提出了对非常规三维面心立方网格(FCC)的三类图片进行拓扑保存并行还原的充分条件。其中一些条件提供了验证给定并行还原是否始终保持拓扑结构的方法,其余条件直接提供了保持拓扑结构的并行还原的删除规则,并使我们有可能生成拓扑结构正确的减薄算法。我们给出了同时删除可保留拓扑的 P 简单点的局部特征,还建立了任意类型二元图片的现有通用充分条件与我们针对 FCC 的新结果之间的关系。
Sufficient Conditions for Topology-Preserving Parallel Reductions on the Face-Centered Cubic Grid
Topology preservation is a crucial issue in parallel reductions that transform binary pictures by changing only a set of black points to white at a time. In this paper, we present sufficient conditions for topology-preserving parallel reductions on the three types of pictures of the unconventional 3D face-centered cubic (FCC) grid. Some conditions provide methods of verifying that a given parallel reduction always preserves the topology, and the remaining ones directly provide deletion rules of topology-preserving parallel reductions, and make us possible to generate topologically correct thinning algorithms. We give local characterizations of P-simple points, whose simultaneous deletion preserves the topology, and the relationships among the existing universal sufficient conditions for arbitrary types of binary pictures and our new FCC-specific results are also established.
期刊介绍:
The Journal of Mathematical Imaging and Vision is a technical journal publishing important new developments in mathematical imaging. The journal publishes research articles, invited papers, and expository articles.
Current developments in new image processing hardware, the advent of multisensor data fusion, and rapid advances in vision research have led to an explosive growth in the interdisciplinary field of imaging science. This growth has resulted in the development of highly sophisticated mathematical models and theories. The journal emphasizes the role of mathematics as a rigorous basis for imaging science. This provides a sound alternative to present journals in this area. Contributions are judged on the basis of mathematical content. Articles may be physically speculative but need to be mathematically sound. Emphasis is placed on innovative or established mathematical techniques applied to vision and imaging problems in a novel way, as well as new developments and problems in mathematics arising from these applications.
The scope of the journal includes:
computational models of vision; imaging algebra and mathematical morphology
mathematical methods in reconstruction, compactification, and coding
filter theory
probabilistic, statistical, geometric, topological, and fractal techniques and models in imaging science
inverse optics
wave theory.
Specific application areas of interest include, but are not limited to:
all aspects of image formation and representation
medical, biological, industrial, geophysical, astronomical and military imaging
image analysis and image understanding
parallel and distributed computing
computer vision architecture design.