Two-dimensional Tsallis gray entropy image thresholding using chaotic particle swarm optimization or decomposition
利用混沌PSO或分解的2维Tsallis灰度熵阈值分割

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.