基于剪切波变换的医学图像融合算法
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摘要
剪切波变换是一种新颖的多尺度几何分析工具,具有多分辨率、多方向性、效率较高等优点,比小波变换、曲波变换、轮廓波变换等图像表示方法有独特有的优势。基于剪切波变换提出一种医学图像融合算法,先将原始图像通过剪切波变换分解为低频子带图像和高频方向子带图像,然后采用非负矩阵分解方法融合低频子带系数,再通过深入研究人类视觉系统的特性提出最大视觉能量对比度方法,利用局部对比度和局部区域的能量和进行高频方向子带系数的融合,最后通过剪切波逆变换得到融合图像。两组实验均显示所提出的融合方法在与其余3种融合方法的比较中,采用的5项客观评价指标均有4项指标达到最优值,证明所提出的方法获取的融合图像效果最好。
Shearlet transform is a novel multiscale geometric analysis tool that has many virtue such as multi-resolution,multi-directional,high efficiency and has unique advantages compared with the wavelet transform,curvelet transform and contourlet transform.This paper proposed a novel fusion method for medical image based on shearlet transform.First,two original images were decomposed into different frequency sub-band coefficients by using shearlet.Next,the selection of the low-frequency sub-band coefficient and the high-frequency directional sub-band coefficient were discussed.The method based on non-negative matrix factorization(NMF)was used to fuse the low-frequency sub-band coefficient,and for the high-frequency directional sub-band coefficient,this paper proposed a maximum visual energy contrast method that chose coefficient based on the local contrast and the sum of local regional energy after studying the human visual characteristics closely.At last,the fused image was obtained by performing the inverse shearlet on the combined coefficients.The proposed fusion method was compared with the other three fusion methods in two sets of experiments,and four of the five objective evaluation indicators also have reached the optimal value.In conclusion,the proposed fusion method has a considerable improvement in subjective fusion quality and objective evaluation.
Shearlet transform is a novel multiscale geometric analysis tool that has many virtue such as multi-resolution,multi-directional,high efficiency and has unique advantages compared with the wavelet transform,curvelet transform and contourlet transform.This paper proposed a novel fusion method for medical image based on shearlet transform.First,two original images were decomposed into different frequency sub-band coefficients by using shearlet.Next,the selection of the low-frequency sub-band coefficient and the high-frequency directional sub-band coefficient were discussed.The method based on non-negative matrix factorization(NMF)was used to fuse the low-frequency sub-band coefficient,and for the high-frequency directional sub-band coefficient,this paper proposed a maximum visual energy contrast method that chose coefficient based on the local contrast and the sum of local regional energy after studying the human visual characteristics closely.At last,the fused image was obtained by performing the inverse shearlet on the combined coefficients.The proposed fusion method was compared with the other three fusion methods in two sets of experiments,and four of the five objective evaluation indicators also have reached the optimal value.In conclusion,the proposed fusion method has a considerable improvement in subjective fusion quality and objective evaluation.
引文
[1]陈晓艳,李健楠,王化祥.一种电阻抗图像与CT图像融合方法研究[J].中国生物医学工程学报,2012,30(6):892-896.
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[3]Das S,Kundu MK.NSCT-based multimodal medical imagefusion using pulse-coupled neural network and modified spatialfrequency[J].Medical and Biological Engineering andComputing,2012,50(10):1105-1114.
[4]Li Shutao,Yin Haitao,Fang Leyuan.Group-sparserepresentation with dictionary learning for medical imagedenoising and fusion[J].IEEE Transactions on Bio-medicalEngineering,2012,59(12):3450-3459.
[5]Singh R,Srivastava R,Prakash O,et al.Multimodal medicalimage fusion in dual tree complex wavelet transform domain usingmaximum and average fusion rules[J].Journal of MedicalImaging and Health Informatics,2012,2(2):168-173.
[6]Townsend DW,Beyer T.A combined PET/CT scanner:the pathto true image fusion[J].British journal of Radiology,2002,75(9):S24-S30.
[7]Yang Liu,Guo Baolong,Ni Wei.Multimodality medical imagefusion based on multiscale geometric analysis of contourlettransform[J].Neurocomputing,2008,72(1):203-211.
[8]杨立才,刘延梅,刘欣,等.基于小波包变换的医学图像融合方法[J].中国生物医学工程学报,2009,28(1):12-16.
[9]Guo Kanghui,Labate D.Optimally sparse multidimensionalrepresentation using shearlets[J].SIAM journal on mathematicalanalysis,2008,39(1):298-318.
[10]Kutyniok G,Labate D.Resolution of the wavefront set usingcontinuous shearlets[J].Trans Amer Math Soc,2009,361(5):2719-2754.
[11]Easley G,Labate D,Lim WQ.Sparse directional imagerepresentations using the discrete shearlet transform[J].Appliedand Computational Harmonic Analysis,2008,25(1):25-46.
[12]Candes EJ,Donoho DL.Curvelets:A surprisingly effectivenonadaptive representation for objects with edges[C]//in Curveand Surface Fitting:Saint-Malo,Nashville,USA:VanderbiltUniversity Press,2000:105-120.
[13]Do MN,Vetterli M.The contourlet transform:an efficientdirectional multiresolution image representation[J].IEEETransactions on Image Processing,2005,14(12):2091-2106.
[14]Cunha AL,Zhou J,Do MN.The nonsubsampled contourlettransform:theory,design,and applications[J].IEEETransactions on Image Processing,2006,15(10):3089-3101.
[15]Miao Qiguang,Shi Cheng,Xua Pengfei,et al.A novel algorithmof imagefusion using shearlets[J].Optics Communications,2011,284(6):1540-1547.
[16]郑红,郑晨,闫秀生,陈海霞.基于剪切波变换的可见光与红外图像融合算法[J].仪器仪表学报,2012,33(7):1613-1619.
[17]Lee DD,Seung HS.Learning the parts of objects by non-negativematrix factorization[J].Nature,1999,401(6755):788-791.
[18]Lim WQ.The discrete shearlet transform:A new directionaltransform and compactly supported shearlet frames[J].IEEETransactions on Image Processing,2010,19(5):1166-1180.
[19]Seung D,Lee L.Algorithms for non-negative matrix factorization[J].Advances in Neural Information Processing Systems,2001,13(2):556-562.
[20]苗启广,王宝树.基于非负矩阵分解的多聚焦图像融合研究[J].光学学报,2005,25(6):755-759.
[21]苗启广,王宝树.图像融合的非负矩阵分解算法[J].计算机辅助设计与图形学学报,2005,17(7):2029-2032.
[22]Legge GE,Foley JM.Contrast masking in human vision[J].JOSA,1980,70(12):1458-1471.
[23]Watson AB.DCT quantization matrices visually optimized forindividual images[C]//Human Vision,Visual Processing andDigital Display IV.San Jose:SPIE,1993:202-216.
[24]Watson AB.Efficiency of a model human image code[J].JOSAA,1987,4(12):2401-2417.
[25]Legge GE.A power law for contrast discrimination[J].VisionResearch,1981,21(4):457-467.
[26]http://www.bic.mni.mcgill.ca/brainweb/.
[2]Constantinos S,Pattichis MS,Micheli-Tzanakou E.Medicalimaging fusion applications:An overview[C]//ConferenceRecord of the Thirty-Fifth Asilomar Conference on Signals,Systems and Computers.Pacific Grove:IEEE,2001:1263-1267.
[3]Das S,Kundu MK.NSCT-based multimodal medical imagefusion using pulse-coupled neural network and modified spatialfrequency[J].Medical and Biological Engineering andComputing,2012,50(10):1105-1114.
[4]Li Shutao,Yin Haitao,Fang Leyuan.Group-sparserepresentation with dictionary learning for medical imagedenoising and fusion[J].IEEE Transactions on Bio-medicalEngineering,2012,59(12):3450-3459.
[5]Singh R,Srivastava R,Prakash O,et al.Multimodal medicalimage fusion in dual tree complex wavelet transform domain usingmaximum and average fusion rules[J].Journal of MedicalImaging and Health Informatics,2012,2(2):168-173.
[6]Townsend DW,Beyer T.A combined PET/CT scanner:the pathto true image fusion[J].British journal of Radiology,2002,75(9):S24-S30.
[7]Yang Liu,Guo Baolong,Ni Wei.Multimodality medical imagefusion based on multiscale geometric analysis of contourlettransform[J].Neurocomputing,2008,72(1):203-211.
[8]杨立才,刘延梅,刘欣,等.基于小波包变换的医学图像融合方法[J].中国生物医学工程学报,2009,28(1):12-16.
[9]Guo Kanghui,Labate D.Optimally sparse multidimensionalrepresentation using shearlets[J].SIAM journal on mathematicalanalysis,2008,39(1):298-318.
[10]Kutyniok G,Labate D.Resolution of the wavefront set usingcontinuous shearlets[J].Trans Amer Math Soc,2009,361(5):2719-2754.
[11]Easley G,Labate D,Lim WQ.Sparse directional imagerepresentations using the discrete shearlet transform[J].Appliedand Computational Harmonic Analysis,2008,25(1):25-46.
[12]Candes EJ,Donoho DL.Curvelets:A surprisingly effectivenonadaptive representation for objects with edges[C]//in Curveand Surface Fitting:Saint-Malo,Nashville,USA:VanderbiltUniversity Press,2000:105-120.
[13]Do MN,Vetterli M.The contourlet transform:an efficientdirectional multiresolution image representation[J].IEEETransactions on Image Processing,2005,14(12):2091-2106.
[14]Cunha AL,Zhou J,Do MN.The nonsubsampled contourlettransform:theory,design,and applications[J].IEEETransactions on Image Processing,2006,15(10):3089-3101.
[15]Miao Qiguang,Shi Cheng,Xua Pengfei,et al.A novel algorithmof imagefusion using shearlets[J].Optics Communications,2011,284(6):1540-1547.
[16]郑红,郑晨,闫秀生,陈海霞.基于剪切波变换的可见光与红外图像融合算法[J].仪器仪表学报,2012,33(7):1613-1619.
[17]Lee DD,Seung HS.Learning the parts of objects by non-negativematrix factorization[J].Nature,1999,401(6755):788-791.
[18]Lim WQ.The discrete shearlet transform:A new directionaltransform and compactly supported shearlet frames[J].IEEETransactions on Image Processing,2010,19(5):1166-1180.
[19]Seung D,Lee L.Algorithms for non-negative matrix factorization[J].Advances in Neural Information Processing Systems,2001,13(2):556-562.
[20]苗启广,王宝树.基于非负矩阵分解的多聚焦图像融合研究[J].光学学报,2005,25(6):755-759.
[21]苗启广,王宝树.图像融合的非负矩阵分解算法[J].计算机辅助设计与图形学学报,2005,17(7):2029-2032.
[22]Legge GE,Foley JM.Contrast masking in human vision[J].JOSA,1980,70(12):1458-1471.
[23]Watson AB.DCT quantization matrices visually optimized forindividual images[C]//Human Vision,Visual Processing andDigital Display IV.San Jose:SPIE,1993:202-216.
[24]Watson AB.Efficiency of a model human image code[J].JOSAA,1987,4(12):2401-2417.
[25]Legge GE.A power law for contrast discrimination[J].VisionResearch,1981,21(4):457-467.
[26]http://www.bic.mni.mcgill.ca/brainweb/.