Two-Dimensional Gray Entropy Image Thresholding Based on Particle Swarm Optimization with High Speed Convergence or Decomposition

The method of threshold selection based on two-dimensional maximal Shannon entropy only depends on the probability information from gray histogram of image,and does not immediately consider the uniformity of within-cluster gray scale.Thus a two-dimensional gray entropy thresholding method based on particle swarm optimization(PSO) with high speed convergence or decomposition is proposed.Firstly,gray entropy is defined and the corresponding formulae for threshold selection based on two-dimensional gray entropy is derived.Then,particle swarm optimization algorithm with high speed convergence are used to find the optimal threshold of two-dimensional gray entropy method.The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure.As a result,the computing speed is improved greatly.Finally,the computations of two-dimensional gray entropy are converted into two one-dimensional spaces,which make the computation complexity further reduced from O(L2) to O(L).The experimental results show that,compared with two-dimensional maximal Shannon entropy thresholding based on PSO,the proposed two methods can have much superior segmentation performance and their running time is reduced significantly.