基于函数映射的二维形状内蕴对称检测算法  

Two-dimensional shape intrinsic symmetry detection algorithm based on functional map

作　　者：刘圣军[1,2] 滕子 王海波 刘新儒[1] LIU Shengjun;TENG Zi;WANG Haibo;LIU Xinru(School of Mathematics and Statistics,Central South University,Changsha 410083,China;Institute of Engineering Modeling and Scientific Computing,Central South University,Changsha 410083,China)

机构地区：[1]中南大学数学与统计学院,湖南长沙410083 [2]中南大学工程建模与科学计算研究所,湖南长沙410083

出　　处：《浙江大学学报（理学版）》2023年第6期668-680,共13页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(62172447).

摘　　要：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。To address the problem that the performance of existing methods is unsatisfactory for detecting intrinsic symmetry in two-dimensional shapes,based on the flexible function mapping framework,we propose a spectral optimization method,named FM-2DSISD,to compute dense point maps for two-dimensional intrinsic symmetric shapes.Firstly,we design an algorithm robust to noise to extract sparse feature symmetry point maps.Secondly,using the feature symmetric point maps and the functional map framework,a mathematical model is developed whose optimization objective is to maintain the diagonality and orthogonality of each principal submatrix of the functional map matrix.We prove that the defined optimization objective can preserve the isometry of intrinsic symmetry maps.To solve the formula,we give an alternating iterative algorithm between the spatial and spectral domains via the spectral up-sampling technique.Numerical experiments show that the proposed algorithm performs better than the state-ofthe-art methods on two-dimensional smooth shapes and noisy shapes.

关 键 词：二维形状 内蕴对称 谱方法 函数映射 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]