{"title":"带偏差校正的同心椭圆拟合和基于几何的特殊聚类方法","authors":"Ali Al-Sharadqah, Giuliano Piga","doi":"10.1007/s10851-024-01197-8","DOIUrl":null,"url":null,"abstract":"<p>This paper addresses the problem of fitting concentric ellipses under general assumptions. We study two methods of obtaining an estimator of the concentric ellipse parameters under this model, namely the <i>least squares</i> and the <i>gradient weighted algebraic fits</i>. We address some practical issues in obtaining these estimators. In this paper, we study the statistical properties of those estimators and we developed a refinement with the highest accuracy for each estimator. We also address a practical issue in concentric ellipse fitting, namely, that each observation in the data set should be recognized as belonging to only one of the concentric ellipses. Most well-known clustering methods, such as spectral clustering, fail for this problem. We propose a clustering approach that can effectively be used for the implementation of our model. Our theory has been validated through intensive numerical experiments on synthetic and real data.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Concentric Ellipse Fitting with Bias Correction and Specialized Geometric-Based Clustering Approach\",\"authors\":\"Ali Al-Sharadqah, Giuliano Piga\",\"doi\":\"10.1007/s10851-024-01197-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper addresses the problem of fitting concentric ellipses under general assumptions. We study two methods of obtaining an estimator of the concentric ellipse parameters under this model, namely the <i>least squares</i> and the <i>gradient weighted algebraic fits</i>. We address some practical issues in obtaining these estimators. In this paper, we study the statistical properties of those estimators and we developed a refinement with the highest accuracy for each estimator. We also address a practical issue in concentric ellipse fitting, namely, that each observation in the data set should be recognized as belonging to only one of the concentric ellipses. Most well-known clustering methods, such as spectral clustering, fail for this problem. We propose a clustering approach that can effectively be used for the implementation of our model. Our theory has been validated through intensive numerical experiments on synthetic and real data.</p>\",\"PeriodicalId\":16196,\"journal\":{\"name\":\"Journal of Mathematical Imaging and Vision\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-05-26\",\"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/s10851-024-01197-8\",\"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/s10851-024-01197-8","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}
Concentric Ellipse Fitting with Bias Correction and Specialized Geometric-Based Clustering Approach
This paper addresses the problem of fitting concentric ellipses under general assumptions. We study two methods of obtaining an estimator of the concentric ellipse parameters under this model, namely the least squares and the gradient weighted algebraic fits. We address some practical issues in obtaining these estimators. In this paper, we study the statistical properties of those estimators and we developed a refinement with the highest accuracy for each estimator. We also address a practical issue in concentric ellipse fitting, namely, that each observation in the data set should be recognized as belonging to only one of the concentric ellipses. Most well-known clustering methods, such as spectral clustering, fail for this problem. We propose a clustering approach that can effectively be used for the implementation of our model. Our theory has been validated through intensive numerical experiments on synthetic and real data.
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.