第5卷第6期 智能系统学报 Vol.5 No.6 2010年12月 CAAI Transactions on Intelligent Systems Dec.2010 doi:10.3969/i.issn1673-4785.2010.06.009 灰度熵和混沌粒子群的图像多阈值选取 吴一全12，纪守新 (南京航空航天大学信息科学与技术学院，江苏南京210016；2南京大学计算机软件新技术国家重点实验室，江苏南京 210093)】 摘要：最大Shannon嫡阈值选取方法仅仅依赖于图像灰度直方图的概率信息，而没有直接考虑类内灰度级的均匀 性.为此提出了最大灰度嫡的阈值选取方法.首先给出了灰度嫡的定义及其单阈值选取方法，该灰度嫡与现有的仅 基于直方图分布的最大Shannon嫡不同，直接反映了类内灰度级的均匀性：其次导出了量化图像直方图的灰度熵单 阈值选取公式：最后将灰度熵单阈值选取推广到多阈值选取，提出了相应的快速递推算法，并进一步采用混沌小生 境粒子群优化算法寻找最佳多阈值.实验结果表明，与最大Shannon熵单阙值选取和基于粒子群的最大Shannon熵 多阈值选取方法相比，所提出方法的分割图像边缘、纹理更为准确，视觉效果明显改善 关键词：图像分割：阈值选取：灰度嫡：量化图像直方图：多阙值：混沌小生境粒子群优化 中图分类号：TP391.41;TN911.73文献标志码：A文章编号：16734785(2010)06052208 Multi-threshold selection for an image based on gray entropy and chaotic particle swarm optimization WU Yi-quan'2,JI Shou-xin' (1.School of Information Science and Technology,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China; 2.State Key Laboratory for Novel Software Technology,Nanjing University,Nanjing 210093,China) Abstract:The method of threshold selection based on maximal Shannon entropy depends only on the probability in- formation from a gray image histogram and does not immediately consider the uniformity of the gray scale within the cluster.Considering these facts,a method of threshold selection based on maximal gray entropy was proposed. First,gray entropy was defined and the method of single threshold selection was given.Being different from maxi- mal Shannon entropy based only on histogram distribution,the gray entropy reflects the uniformity of the gray scale immediately within the cluster.Then,the formulae of gray entropy based single threshold selection of a quantized image histogram were derived.Finally,the method of single threshold selection based on gray entropy was extended to multi-threshold selection.A corresponding fast recurring algorithm was proposed.Furthermore,a particle swarm optimization algorithm with a chaotic niche was adopted to find the best multi-threshold.Many experimental results show that,compared with the methods of single threshold selection based on maximal Shannon entropy and multi- threshold selection based on maximal Shannon entropy with particle swarm optimization,segmented images of the suggested method are more accurate in edge and texture,and their visual effect is improved significantly. Keywords:image segmentation;threshold selection;gray entropy;quantified image histogram;multi-threshold; particle swarm optimization of chaotic niche 图像分割就是把图像中具有特定含义的不同区 以获得最佳分割效果.在较早提出并进行定性和定 域分割开来，每一个区域都满足某种特性的一致性。 量比较研究的、有代表性的阈值选取方法中，由Ka 目标检测、特征提取和目标识别等，都依赖于图像 pur等人[)提出的最大Shannon熵阈值选取方法，通 分割的质量12].阈值分割是简单有效、应用广泛且 过引人信息论中的Shannon熵准则寻找最佳阈值， 易于实现的图像分割方法，其关键是自动选取阈值 因能产生较好的分割效果且简单有效，成为人们最 为关注的阈值选取方法之一.单阈值分割是通过一 收稿日期：201004-12. 个阈值把图像分成目标和背景2类区域，但实际图 基金项目：国家自然科学基金资助项目(60872065)；航空科学基金资 助项目(20105152026)；南京大学计算机软件新技术国家 像中往往含有灰度明显不同的多类目标.当最大 重点实验室开放基金资助项目(KFKT2010B17). Shannon熵单阈值选取推广到多阈值选取时[4]，导 通信作者：吴一全.E-mail:nuaaimage@yahoo.com.cm