现有最大Shannon熵或Tsallis熵阈值选取方法没有从类内灰度均匀性出发,而仅依据图像灰度直方图,并且Tsallis熵法的分割效果通常优于Shannon熵法。为此,提出了基于混沌粒子群优化(PSO)和基于分解的两种2维Tsallis灰度熵阈值分割方法。首先,给出了1维Tsallis灰度熵阈值选取方法并将其推广到2维,导出了相应的2维Tsallis灰度熵阈值选取公式及其递推算法;其次,利用混沌PSO算法搜寻2维Tsallis灰度熵法的最佳阈值,并采用递推方式去除迭代过程中适应度函数的冗余运算,大大提高了运行速度;最后,将2维Tsallis灰度熵阈值选取方法的运算转化为两个1维Tsallis灰度熵法的运算,计算复杂度从O(L²)进一步降低到O(L)。实验结果表明,与2维最大Shannon熵法、2维最大Tsallis熵法及2维Tsallis交叉熵法相比,所提出的两种方法可以大幅提高图像分割质量和算法运行速度。

The method of threshold selection based on two-dimensional maximal Shannon or Tsallis entropy only depends on the probability information from gray histogram of an image, and does not immediately consider the uniformity of within-cluster gray scale. The segmentation effect of the Tsallis entropy method is superior to that of the Shannon entropy method. Thus, a two-dimensional Tsallis gray entropy thresholding method based on chaotic particle swarm optimization(PSO) or decomposition is proposed. First, a one-dimensional thresholding method based on Tsallis gray entropy is given and extended to the two-dimensional case. The corresponding formulae and its recursive algorithm for threshold selection based on the two-dimensional Tsallis gray entropy are derived. Then a chaotic particle swarm optimization algorithm is used to find the optimal threshold of the two-dimensional Tsallis gray entropy method. The recursive algorithm is adopted to avoid the repetitive computation of the fitness function in an iterative procedure. As a result, the computing speed is improved greatly. Finally, the computations of threshold selection method based on two-dimensional Tsallis gray entropy are converted into two one-dimensional spaces, which further reduces the computational complexity from O(L²) to O(L). The experimental results show that, compared with the two-dimensional maximal Shannon entropy method, the two-dimensional maximal Tsallis entropy method and the two-dimensional Tsallis cross entropy method, the two methods proposed in this paper can significantly improve image segmentation performance and algorithmic running speed.