河北工业大学学报JOURNALOFHEBEIUNIVERSITYOFTECHNOLOGY2023年2月February2023第52卷第1期Vol.52No.1提高工件表面缺陷提取鲁棒性的改进低秩矩阵恢复算法张晶，刘丽冰，黄智坤，袁军，杨泽青（河北工业大学机械工程学院，天津300401）摘要针对传统的工件缺陷提取方法存在鲁棒性差的问题，提出一种基于同态滤波的改进低秩矩阵恢复算法。首先使用同态滤波方法增强光照分量、抑制工件反射分量，减小光照不均和工件强反光产生伪缺陷的影响；然后应用鲁棒主成分分析模型将工件表面缺陷提取问题转换为低秩背景矩阵和稀疏缺陷矩阵分离的低秩矩阵恢复问题；最后使用非精确拉格朗日乘子法对由鲁棒主成分分析模型转化的凸优化模型进行求解。以带有凹坑、划痕缺陷的轴类工件为样本，通过计算F-measure值完成方法验证，实验结果表明：在不同光照强度的实验条件下，离散傅里叶算法提取凹坑缺陷和划痕缺陷的平均F值分别为0.4357和0.3819；本文提出算法提取凹坑缺陷和划痕缺陷的平均F值分别为0.7260和0.7169，结果验证了所提算法的有效性和较高鲁棒性。关键词缺陷提取；低秩矩阵恢复；同态滤波；非精确拉格朗日乘子法；鲁棒性中图分类号TH164文献标志码AImprovedlow-rankmatrixrestorationalgorithmforimprovingtherobustnessofworkpiecesurfacedefectextractionZHANGJing,LIULibing,HUANGZhikun,YUANJun,YANGZeqing（SchoolofMechanicalEngineering,HebeiUniversityofTechnology,Tianjin300401,China）AbstractAnimprovedlowrankmatrixrecoveryalgorithmbasedonhomomorphicfilteringwasproposedtosolvetheproblemofpoorrobustnessinthetraditionalmethodsofextractingworkpiecedefects.Firstly,thehomomorphicfilteringmethodwasusedtoenhancetheilluminationcomponentandsuppressthereflectioncomponentoftheworkpiecetore⁃ducetheinfluenceofilluminationunevennessandstrongreflectionoftheworkpiecetoproducefalsedefects.Thentherobustprincipalcomponentanalysismodelwasusedtotransformthesurfacedefectextractionproblemintothelow-rankmatrixrecoveryproblemseparatedfromthelow-rankbackgroundmatrixandthesparsedefectmatrix.Finally,animpre⁃ciseLagrangianmultipliermethodwasusedtosolvetheconvexoptimizationmodeltransformedfromtherobustprincipalcomponentanalysismodel.Withindentation,scratchdefectssuchasaxialworkpieceassample,bycalcul...
