第13卷第1期 智能系统学报 Vol.13 No.I 2018年2月 CAAI Transactions on Intelligent Systems Feb.2018 D0:10.11992/tis.201607004 网络出版t地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20170626.1739.008.html 利用混沌布谷鸟优化的二维Renyi灰度熵图像阈值选取 马英辉2，吴一全145 (1.南京航空航天大学电子信息工程学院，江苏南京211106：2.宿迁学院信息工程学院，江苏宿迁223800,3.西华 大学制造与自动化省高校重点实验室，四川成都610039,4.华中科技大学数字制造装备与技术国家重点实验室，湖 北武汉430074,5.安徽理工大学煤矿安全高效开采省部共建教育部重点实验室，安徽淮南232001) 摘要：为了进一步降低现有的Renyi嫡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Ryi灰度嫡阈值选取公式，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Ryi灰度嫡阈值选取公式，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嫡法、基于粒子群的二维Renyi嫡法、基于混沌粒子群 的二维Tsallis灰度嫡法、基于布谷鸟算法的二维Reyi灰度嫡法相比，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。 关键词：图像分割：阈值选取；布谷鸟算法：Renyi灰度嫡：灰度-梯度二维直方图：混沌优化：Arimoto嫡：Tsallis灰度嫡 中图分类号：TP391.41文献标志码：A文章编号：1673-4785(2018)01-0152-07 中文引用格式：马英辉，吴一全.利用混沌布谷鸟优化的二维Reyi灰度熵图像阈值选取.智能系统学报，2018.13(1)：152-158. 英文引用格式：MA Yinghui,.WU Yiquan..Two-dimensional Renyi--gray-entropy image threshold selection based on chaotic cuckoo search optimization[J].CAAI transactions on intelligent systems,2018,13(1):152-158. Two-dimensional Renyi-gray-entropy image threshold selection based on chaotic cuckoo search optimization MA Yinghui2,WU Yiquan'345 (1.College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 211 106,China; 2.School of Information Engineering,Suqian College,Sugian 223800,China;3.Key Laboratory of Manufacturing Automation, Xihua University,Chengdu 610039,China;4.State Key Laboratory of Digital Manufacturing Equipment&Technology,Huazhong University of Science and Technology,Wuhan 430074,China;5.Key Laboratory of Safety and High-efficiency Coal Mining,Min istry of Education,Anhui University of Science and Technology,Huainan,232001,China) Abstract: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-en- tropy 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 Tsallis- gray-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. Keywords:image segmentation;threshold selection;cuckoo search algorithm;Renyi gray entropy;gray-gradient two- dimensional histogram;chaotic optimization;Arimoto entropy;Tsallis gray entropy 阈值分割1因为简单有效且快速实用，可广泛 收稿日期：2016-07-05.网络出版日期：2017-06-26. 基金项目：西华大学制造与自动化省高校重点实验室开放课题 应用于刀具磨损、火焰、工业CT等一系列机器视觉 (S2j2014-028):华中科技大学数字制造装备与技术国家 重点实验室开放课题(DMETKF20140I0):安徽理工大 检测领域。其关键是依据目标和背景在图像中的不 学煤矿旷安全高效开采省部共建教育部重点实验室开放 课题YBSYS2014102). 同灰度信息，快速确定最佳阈值，将图像中感兴趣 通信作者：吴一全.Email:nuaaimage(@163.com. 的目标从背景中提取出来，从而得到清晰的边缘。DOI: 10.11992/tis.201607004 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20170626.1739.008.html 利用混沌布谷鸟优化的二维 Renyi 灰度熵图像阈值选取 马英辉1,2，吴一全1,3,4,5 （1. 南京航空航天大学 电子信息工程学院，江苏 南京 211106; 2. 宿迁学院 信息工程学院，江苏 宿迁 223800; 3. 西华 大学 制造与自动化省高校重点实验室，四川 成都 610039; 4. 华中科技大学 数字制造装备与技术国家重点实验室，湖 北 武汉 430074; 5. 安徽理工大学 煤矿安全高效开采省部共建教育部重点实验室，安徽 淮南 232001） 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。 关键词：图像分割；阈值选取；布谷鸟算法；Renyi 灰度熵；灰度-梯度二维直方图；混沌优化；Arimoto 熵；Tsallis 灰度熵 中图分类号：TP391.41 文献标志码：A 文章编号：1673−4785(2018)01−0152−07 中文引用格式：马英辉, 吴一全. 利用混沌布谷鸟优化的二维 Renyi 灰度熵图像阈值选取[J]. 智能系统学报, 2018, 13(1): 152–158. 英文引用格式：MA Yinghui, WU Yiquan. Two-dimensional Renyi-gray-entropy image threshold selection based on chaotic cuckoo search optimization[J]. CAAI transactions on intelligent systems, 2018, 13(1): 152–158. Two-dimensional Renyi-gray-entropy image threshold selection based on chaotic cuckoo search optimization MA Yinghui1,2 ，WU Yiquan1,3,4,5 (1. College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China; 2. School of Information Engineering, Suqian College, Suqian 223800, China; 3. Key Laboratory of Manufacturing & Automation, Xihua University, Chengdu 610039, China; 4. State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology, Wuhan 430074, China; 5. Key Laboratory of Safety and High-efficiency Coal Mining, Min￾istry of Education, Anhui University of Science and Technology, Huainan, 232001, China) Abstract: 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-en￾tropy 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 Tsallis￾gray-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. Keywords: image segmentation; threshold selection; cuckoo search algorithm; Renyi gray entropy; gray-gradient two￾dimensional histogram; chaotic optimization; Arimoto entropy; Tsallis gray entropy 阈值分割[1-4]因为简单有效且快速实用，可广泛 应用于刀具磨损、火焰、工业 CT 等一系列机器视觉 检测领域。其关键是依据目标和背景在图像中的不 同灰度信息，快速确定最佳阈值，将图像中感兴趣 的目标从背景中提取出来，从而得到清晰的边缘。 收稿日期：2016−07−05. 网络出版日期：2017−06−26. 基金项目：西华大学制造与自动化省高校重点实验室开放课题 (S2jj2014-028)；华中科技大学数字制造装备与技术国家 重点实验室开放课题 (DMETKF2014010)；安徽理工大 学煤矿安全高效开采省部共建教育部重点实验室开放 课题 (JYBSYS2014102). 通信作者：吴一全. Email：nuaaimage@163.com. 第 13 卷第 1 期 智 能 系 统 学 报 Vol.13 No.1 2018 年 2 月 CAAI Transactions on Intelligent Systems Feb. 2018