基于切线表示法的曲线弹性形状逻辑回归模型

Pub Date : 2024-01-12 DOI:10.1007/s42952-023-00252-1
Tae-Young Heo, Joon Myoung Lee, Myung Hun Woo, Hyeongseok Lee, Min Ho Cho
{"title":"基于切线表示法的曲线弹性形状逻辑回归模型","authors":"Tae-Young Heo, Joon Myoung Lee, Myung Hun Woo, Hyeongseok Lee, Min Ho Cho","doi":"10.1007/s42952-023-00252-1","DOIUrl":null,"url":null,"abstract":"<p>Shape analysis is widely used in many application areas such as computer vision, medical and biological studies. One challenge to analyze the shape of an object in an image is its invariant property to shape-preserving transformations. To measure the distance or dissimilarity between two different shapes, we worked with the square-root velocity function (SRVF) representation and the elastic metric. Since shapes are inherently high-dimensional in a nonlinear space, we adopted a tangent space at the mean shape and a few principal components (PCs) on the linearized space. We proposed classification methods based on logistic regression using these PCs and tangent vectors with the elastic net penalty. We then compared its performance with other model-based methods for shape classification in application to shape of algae in watersheds as well as simulated data generated by the mixture of von Mises-Fisher distributions.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Logistic regression models for elastic shape of curves based on tangent representations\",\"authors\":\"Tae-Young Heo, Joon Myoung Lee, Myung Hun Woo, Hyeongseok Lee, Min Ho Cho\",\"doi\":\"10.1007/s42952-023-00252-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Shape analysis is widely used in many application areas such as computer vision, medical and biological studies. One challenge to analyze the shape of an object in an image is its invariant property to shape-preserving transformations. To measure the distance or dissimilarity between two different shapes, we worked with the square-root velocity function (SRVF) representation and the elastic metric. Since shapes are inherently high-dimensional in a nonlinear space, we adopted a tangent space at the mean shape and a few principal components (PCs) on the linearized space. We proposed classification methods based on logistic regression using these PCs and tangent vectors with the elastic net penalty. We then compared its performance with other model-based methods for shape classification in application to shape of algae in watersheds as well as simulated data generated by the mixture of von Mises-Fisher distributions.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s42952-023-00252-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42952-023-00252-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

形状分析广泛应用于计算机视觉、医学和生物研究等多个领域。分析图像中物体的形状所面临的一个挑战是其对保形变换的不变性。为了测量两个不同形状之间的距离或差异,我们使用了平方根速度函数(SRVF)表示法和弹性度量。由于形状在非线性空间中本身就是高维的,因此我们在平均形状处采用了切线空间,并在线性化空间上采用了几个主成分(PC)。我们提出了基于逻辑回归的分类方法,使用这些 PC 和切向量以及弹性网惩罚。然后,我们将其与其他基于模型的形状分类方法进行了性能比较,并将其应用于流域中藻类的形状以及由 von Mises-Fisher 分布混合生成的模拟数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Logistic regression models for elastic shape of curves based on tangent representations

分享
查看原文
Logistic regression models for elastic shape of curves based on tangent representations

Shape analysis is widely used in many application areas such as computer vision, medical and biological studies. One challenge to analyze the shape of an object in an image is its invariant property to shape-preserving transformations. To measure the distance or dissimilarity between two different shapes, we worked with the square-root velocity function (SRVF) representation and the elastic metric. Since shapes are inherently high-dimensional in a nonlinear space, we adopted a tangent space at the mean shape and a few principal components (PCs) on the linearized space. We proposed classification methods based on logistic regression using these PCs and tangent vectors with the elastic net penalty. We then compared its performance with other model-based methods for shape classification in application to shape of algae in watersheds as well as simulated data generated by the mixture of von Mises-Fisher distributions.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信