Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法)
针对现有的二维形状内蕴对称检测方法表现欠佳的问题，提出了基于函数映射的二维形状内蕴对称稠密点对应谱优化（FM-2DSISD）方法。首先，设计了对噪声数据鲁棒的稀疏特征对称点对提取算法。其次，利用特征对称点对和函数映射框架，建立了以保持函数映射矩阵每个主子矩阵对角正交性为优化目标的数学模型，证明了该优化目标能保持内蕴对称映射的等距性。借助谱上采样技术，通过频谱域和空间域交替迭代优化函数映射矩阵和逐点映射矩阵。数值实验表明，FM-2DSISD方法对二维光滑形状和噪声形状的检测效果均优于现有检测方法。...
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2023-11-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2023.06.002 |
| _version_ | 1797232891222032384 |
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| author | 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) |
| author_facet | 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) |
| author_sort | 刘圣军(LIU Shengjun) |
| collection | DOAJ |
| description | 针对现有的二维形状内蕴对称检测方法表现欠佳的问题，提出了基于函数映射的二维形状内蕴对称稠密点对应谱优化（FM-2DSISD）方法。首先，设计了对噪声数据鲁棒的稀疏特征对称点对提取算法。其次，利用特征对称点对和函数映射框架，建立了以保持函数映射矩阵每个主子矩阵对角正交性为优化目标的数学模型，证明了该优化目标能保持内蕴对称映射的等距性。借助谱上采样技术，通过频谱域和空间域交替迭代优化函数映射矩阵和逐点映射矩阵。数值实验表明，FM-2DSISD方法对二维光滑形状和噪声形状的检测效果均优于现有检测方法。 |
| first_indexed | 2024-04-24T16:07:28Z |
| format | Article |
| id | doaj.art-3f69e748a9ad45fe9f15d3733817b9a6 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:07:28Z |
| publishDate | 2023-11-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-3f69e748a9ad45fe9f15d3733817b9a62024-04-01T01:52:11ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972023-11-0150666868010.3785/j.issn.1008-9497.2023.06.002Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法)刘圣军(LIU Shengjun)0https://orcid.org/0000-0002-3222-5656刘圣军(LIU Shengjun)1刘圣军(LIU Shengjun)2https://orcid.org/0000-0002-6612-7528刘圣军(LIU Shengjun)31School of Mathematics and Statistics， Central South University， Changsha 410083， China(1中南大学 数学与统计学院，湖南 长沙 410083)1School of Mathematics and Statistics， Central South University， Changsha 410083， China(1中南大学 数学与统计学院，湖南 长沙 410083)1School of Mathematics and Statistics， Central South University， Changsha 410083， China(1中南大学 数学与统计学院，湖南 长沙 410083)1School of Mathematics and Statistics， Central South University， Changsha 410083， China(1中南大学 数学与统计学院，湖南 长沙 410083)针对现有的二维形状内蕴对称检测方法表现欠佳的问题，提出了基于函数映射的二维形状内蕴对称稠密点对应谱优化（FM-2DSISD）方法。首先，设计了对噪声数据鲁棒的稀疏特征对称点对提取算法。其次，利用特征对称点对和函数映射框架，建立了以保持函数映射矩阵每个主子矩阵对角正交性为优化目标的数学模型，证明了该优化目标能保持内蕴对称映射的等距性。借助谱上采样技术，通过频谱域和空间域交替迭代优化函数映射矩阵和逐点映射矩阵。数值实验表明，FM-2DSISD方法对二维光滑形状和噪声形状的检测效果均优于现有检测方法。https://doi.org/10.3785/j.issn.1008-9497.2023.06.002 |
| spellingShingle | 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) 刘圣军(LIU Shengjun) Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法) Zhejiang Daxue xuebao. Lixue ban |
| title | Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法) |
| title_full | Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法) |
| title_fullStr | Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法) |
| title_full_unstemmed | Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法) |
| title_short | Two-dimensional shape intrinsic symmetry detection algorithm based on functional map(基于函数映射的二维形状内蕴对称检测算法) |
| title_sort | two dimensional shape intrinsic symmetry detection algorithm based on functional map 基于函数映射的二维形状内蕴对称检测算法 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2023.06.002 |
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