{"title":"定向数据的数学形态学","authors":"Konstantin Hauch, Claudia Redenbach","doi":"10.1007/s10851-024-01210-0","DOIUrl":null,"url":null,"abstract":"<p>We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical Morphology on Directional Data\",\"authors\":\"Konstantin Hauch, Claudia Redenbach\",\"doi\":\"10.1007/s10851-024-01210-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.</p>\",\"PeriodicalId\":16196,\"journal\":{\"name\":\"Journal of Mathematical Imaging and Vision\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-09-06\",\"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/s10851-024-01210-0\",\"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/s10851-024-01210-0","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}
We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.
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.
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