利用混沌布谷鸟优化的二维Renyi灰度熵图像阈值选取
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摘要
为了进一步降低现有的Renyi熵阈值法的计算复杂度,提出了基于混沌布谷鸟算法和二维Renyi灰度熵的阈值选取。首先,引入一维Renyi灰度熵阈值选取公式,建立基于像素灰度和邻域梯度的二维直方图,推导出基于该直方图的二维Renyi灰度熵阈值选取公式,通过快速递推公式来减少阈值准则函数的计算量;最后,采用混沌布谷鸟算法搜索最优阈值来完成图像分割。结果表明,与二维Arimoto熵法、基于粒子群的二维Renyi熵法、基于混沌粒子群的二维Tsallis灰度熵法、基于布谷鸟算法的二维Renyi灰度熵法相比,所提出的方法能够准确实现图像分割,且运算速度有所提升。
To further reduce the computational complexity of existing thresholding methods based on Renyi's entropy,in this paper, we propose a method for threshold selection based on 2-D Renyi-gray-entropy image threshold selection and chaotic cuckoo search optimization. First, we derive the formula for a 1-D Renyi-gray-entropy threshold selection.Then, we build a 2-D histogram based on the grayscale and gray-gradient and derive a formula for 2-D Renyi-gray-entropy threshold selection based on this histogram. We use fast recursive algorithms to eliminate redundant computation in the threshold-selection criterion function. Finally, to achieve image segmentation, we search for the optimal threshold using the chaotic cuckoo search algorithm. The experimental results show that, compared with 2-D Arimoto-entropy thresholding method, the 2-D Renyi-entropy thresholding method based on particle swarm optimization, the 2-D Tsallisgray-entropy thresholding method using chaotic particle swarm, and the 2-D Renyi-gray-entropy thresholding method based on the cuckoo search, our proposed method can segment objects more accurately and has a higher running speed.
To further reduce the computational complexity of existing thresholding methods based on Renyi's entropy,in this paper, we propose a method for threshold selection based on 2-D Renyi-gray-entropy image threshold selection and chaotic cuckoo search optimization. First, we derive the formula for a 1-D Renyi-gray-entropy threshold selection.Then, we build a 2-D histogram based on the grayscale and gray-gradient and derive a formula for 2-D Renyi-gray-entropy threshold selection based on this histogram. We use fast recursive algorithms to eliminate redundant computation in the threshold-selection criterion function. Finally, to achieve image segmentation, we search for the optimal threshold using the chaotic cuckoo search algorithm. The experimental results show that, compared with 2-D Arimoto-entropy thresholding method, the 2-D Renyi-entropy thresholding method based on particle swarm optimization, the 2-D Tsallisgray-entropy thresholding method using chaotic particle swarm, and the 2-D Renyi-gray-entropy thresholding method based on the cuckoo search, our proposed method can segment objects more accurately and has a higher running speed.
引文
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[3]吴一全,孟天亮,王凯.基于斜分倒数交叉熵和蜂群优化的火焰图像阈值选取[J].光学精密工程,2014,22(1):235–243.WU Yiquan,MENG Tianliang,WANG Kai.Threshold selection of flame image based on reciprocal cross entropy and bee colony optimization[J].Optics and precision engineering,2014,22(1):235–243.
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[5]YIN Jun,WU Yiquan,ZHU Li.Multi-thresholding based on symmetric Tsallis-cross entropy and particle swarm optimization[J].Advanced materials research,2013,760-762:1457–1461.
[6]LIU Yaoyong,LI Shuguang.Two-dimensional arimoto entropy image thresholding based on ellipsoid region search strategy[C]//Proceedings of 2010 International Conference on Multimedia Technology.Ningbo,China,2010:1–4.
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[9]曹建农.图像分割的熵方法综述[J].模式识别与人工智能,2012,25(6):958–971.CAO Jiannong.Review on image segmentation based on entropy[J].Pattern recognition and artificial intelligence,2012,25(6):958–971.
[10]张弘,范九伦.二维Arimoto熵直线型阈值分割法[J].光子学报,2013,42(2):234–240.ZHANG Hong,FAN Jiulun.Two-dimensional Arimoto entropy linear-type threshold segmentation method[J].Acta photonica sinica,2013,42(2):234–240.
[11]吴一全,王凯,曹鹏祥.蜂群优化的二维非对称Tsallis交叉熵图像阈值选取[J].智能系统学报,2015,10(1):103–112.WU Yiquan,WANG Kai,CAO Pengxiang.Two-dimensional asymmetric Tsallis cross entropy image threshold selection using bee colony optimization[J].CAAI transactions on intelligent systems,2015,10(1):103–112.
[12]吴一全,吴诗婳,张晓杰.利用混沌PSO或分解的2维Tsallis灰度熵阈值分割[J].中国图象图形学报,2012,17(8):902–910.WU Yiquan,WU Shihua,ZHANG Xiaojie.Two-dimensional Tsallis gray entropy image thresholding using chaotic particle swarm optimization or decomposition[J].Journal of image and graphics,2012,17(8):902–910.
[13]SARKAR S,DAS S.Multilevel image thresholding based on 2D histogram and maximum tsallis entropy—a differential evolution approach[J].IEEE transactions on image processing,2013,22(12):4788–4797.
[14]潘喆,吴一全.二维Renyi熵图像阈值选取快速递推算法[J].中国体视学与图像分析,2007,12(2):93–97.PAN Zhe,WU Yiquan.Fast recurring algorithms of image thresholding based on two-dimensional Renyi’s entropy[J].Chinese journal of stereology and image analysis,2007,12(2):93–97.
[15]顾晓清,孙玉强,侯振杰.鲁棒的二维Renyi熵图像阈值分割快速算法[J].计算机科学,2012,39(9):284–288.GU Xiaoqing,SUN Yuqiang,HOU Zhenjie.Fast robust thresholding method based on two-dimensional Renyi’s entropy[J].Computer science,2012,39(9):284–288.
[16]TEIXEIRA A,MATOS A,ANTUNES L.Conditional rényi entropies[J].IEEE transactions on information theory,2012,58(7):4273–4277.
[17]雷博.二维直线型Renyi熵阈值分割方法[J].西安邮电学院学报,2010,15(3):19–22.LEI Bo.Two-dimensional thresholding method based on linear-type Renyi entropy[J].Journal of Xi’an university of posts and telecommunications,2010,15(3):19–22.
[18]YANG X S,DEB S.Cuckoo search via Lévy flights[C]//Proceedings of 2009 World Congress on Nature and Biologically Inspired Computing.Coimbatore,India,2009:210–214.
[19]周欢,李煜.具有动态惯性权重的布谷鸟搜索算法[J].智能系统学报,2015,10(4):645–651.ZHOU Huan,LI Yu.Cuckoo search algorithm with dynamic inertia weight[J].CAAI transactions on intelligent systems,2015,10(4):645–651.
[20]YANG X S,DEB S.Engineering optimisation by cuckoo search[J].International journal of mathematical modelling and numerical optimisation,2010,1(4):330–343.
[2]吴一全,孟天亮,吴诗婳.图像阈值分割方法研究进展20年(1994—2014)[J].数据采集与处理,2015,30(01):1–23.WU Yiquan,MENG Tianliang,WU Shihua.Research progress of image thresholding methods in recent 20 years(1994-2014)[J].Journal of data acquisition and processing,2015,30(01):1–23.
[3]吴一全,孟天亮,王凯.基于斜分倒数交叉熵和蜂群优化的火焰图像阈值选取[J].光学精密工程,2014,22(1):235–243.WU Yiquan,MENG Tianliang,WANG Kai.Threshold selection of flame image based on reciprocal cross entropy and bee colony optimization[J].Optics and precision engineering,2014,22(1):235–243.
[4]吴一全,张金矿.二维直方图θ-划分最大平均离差阈值分割算法[J].自动化学报,2010,36(5):634–643.WU Yiquan,ZHANG Jinkuang.Image thresholding based on two-dimensional histogramθ-division and maximum between-cluster deviation criterion[J].Acta automatica sinica,2010,36(5):634–643.
[5]YIN Jun,WU Yiquan,ZHU Li.Multi-thresholding based on symmetric Tsallis-cross entropy and particle swarm optimization[J].Advanced materials research,2013,760-762:1457–1461.
[6]LIU Yaoyong,LI Shuguang.Two-dimensional arimoto entropy image thresholding based on ellipsoid region search strategy[C]//Proceedings of 2010 International Conference on Multimedia Technology.Ningbo,China,2010:1–4.
[7]MAHMOUDI L,ZAART A E.A survey of entropy image thresholding techniques[C]//Proceedings of the 2nd International Conference on Advances in Computational Tools for Engineering Applications.Beirut,Lebanon,2012:204–209.
[8]朱磊.自适应阈值分割技术及在工业视觉检测中的应用[D].无锡:江南大学,2014.ZHU Lei.Adaptive threshold segmentation technology and its application in industrial visual inspection[D].Wuxi:Jiangnan University,2014.
[9]曹建农.图像分割的熵方法综述[J].模式识别与人工智能,2012,25(6):958–971.CAO Jiannong.Review on image segmentation based on entropy[J].Pattern recognition and artificial intelligence,2012,25(6):958–971.
[10]张弘,范九伦.二维Arimoto熵直线型阈值分割法[J].光子学报,2013,42(2):234–240.ZHANG Hong,FAN Jiulun.Two-dimensional Arimoto entropy linear-type threshold segmentation method[J].Acta photonica sinica,2013,42(2):234–240.
[11]吴一全,王凯,曹鹏祥.蜂群优化的二维非对称Tsallis交叉熵图像阈值选取[J].智能系统学报,2015,10(1):103–112.WU Yiquan,WANG Kai,CAO Pengxiang.Two-dimensional asymmetric Tsallis cross entropy image threshold selection using bee colony optimization[J].CAAI transactions on intelligent systems,2015,10(1):103–112.
[12]吴一全,吴诗婳,张晓杰.利用混沌PSO或分解的2维Tsallis灰度熵阈值分割[J].中国图象图形学报,2012,17(8):902–910.WU Yiquan,WU Shihua,ZHANG Xiaojie.Two-dimensional Tsallis gray entropy image thresholding using chaotic particle swarm optimization or decomposition[J].Journal of image and graphics,2012,17(8):902–910.
[13]SARKAR S,DAS S.Multilevel image thresholding based on 2D histogram and maximum tsallis entropy—a differential evolution approach[J].IEEE transactions on image processing,2013,22(12):4788–4797.
[14]潘喆,吴一全.二维Renyi熵图像阈值选取快速递推算法[J].中国体视学与图像分析,2007,12(2):93–97.PAN Zhe,WU Yiquan.Fast recurring algorithms of image thresholding based on two-dimensional Renyi’s entropy[J].Chinese journal of stereology and image analysis,2007,12(2):93–97.
[15]顾晓清,孙玉强,侯振杰.鲁棒的二维Renyi熵图像阈值分割快速算法[J].计算机科学,2012,39(9):284–288.GU Xiaoqing,SUN Yuqiang,HOU Zhenjie.Fast robust thresholding method based on two-dimensional Renyi’s entropy[J].Computer science,2012,39(9):284–288.
[16]TEIXEIRA A,MATOS A,ANTUNES L.Conditional rényi entropies[J].IEEE transactions on information theory,2012,58(7):4273–4277.
[17]雷博.二维直线型Renyi熵阈值分割方法[J].西安邮电学院学报,2010,15(3):19–22.LEI Bo.Two-dimensional thresholding method based on linear-type Renyi entropy[J].Journal of Xi’an university of posts and telecommunications,2010,15(3):19–22.
[18]YANG X S,DEB S.Cuckoo search via Lévy flights[C]//Proceedings of 2009 World Congress on Nature and Biologically Inspired Computing.Coimbatore,India,2009:210–214.
[19]周欢,李煜.具有动态惯性权重的布谷鸟搜索算法[J].智能系统学报,2015,10(4):645–651.ZHOU Huan,LI Yu.Cuckoo search algorithm with dynamic inertia weight[J].CAAI transactions on intelligent systems,2015,10(4):645–651.
[20]YANG X S,DEB S.Engineering optimisation by cuckoo search[J].International journal of mathematical modelling and numerical optimisation,2010,1(4):330–343.