最大倒数熵/倒数灰度熵多阈值选取

现有的基于Shannon熵的阈值选取方法存在无定义值和零值的缺陷，并且没有考虑目标和背景类内灰度的均匀性。为此，本文针对多目标（背景）图像分割问题，提出了基于最大倒数熵/倒数灰度熵和自适应双粒子群优化（Adaptive Chaotic Variation Particle Swarm Optimization, ACPSO）的多阈值选取方法。首先将最大倒数熵单阈值选取推广到多阈值选取；然后定义了倒数灰度熵，导出了基于最大倒数灰度熵的单阈值和多阈值选取公式；最后给出最大倒数熵/倒数灰度熵多阈值选取的ACPSO算法步骤，实现对多个阈值快速精确地寻优。实验结果表明，与现有的同类方法—基于最大Shannon熵和粒子群优化（Particle Swarms Optimization, PSO）的多阈值选取方法相比，本文提出的方法有明显的优势，已应用于红外弱小目标检测中的阈值分割和卫星云图识别中的数字云图分割，取得了极佳的分割效果。 

Multi-threshold Selection Using Maximum Reciprocal Entropy/Reciprocal Gray Entropy

The existing threshold selection methods based on Shannon entropy have the defects of undefined value and zero value, and they do not consider the uniformity of the gray scale within the object cluster and background cluster. In view of the above problems, the methods of multi-threshold selection based on maximum reciprocal entropy / reciprocal gray entropy and adaptive chaotic variation particle swarm optimization (ACPSO) are proposed for images including multiple objects or backgrounds in this paper. Firstly, the method of single threshold selection based on maximum reciprocal entropy is extended to multi-threshold selection. Then, reciprocal gray entropy is defined. The formulae of single threshold selection and multi-threshold selection based on maximum reciprocal gray entropy are derived. Finally, to find the optimal multiple thresholds quickly and accurately, the algorithm steps of multi-threshold selection based on reciprocal entropy / reciprocal gray entropy and ACPSO are given. The experimental results show that, compared with the existing related method, which is the method of multi-threshold selection based on maximum Shannon entropy and particle swarms optimization (PSO), the methods proposed in this paper have obvious advantages. Moreover, the methods have been used for image segmentation in infrared small target detection and satellite cloud image recognition, and they have excellent segmentation effect.