2D Direction Histogram-Based Rényi Entropic Multilevel Thresholding

2D histogram-based thresholding methods, in which the histogram is computed from local image features, have better performance than 1D histogram-based methods, but they take much more computation time. In this paper, we present a Rényi entropic multilevel thresholding (REMT) method based on a 2D direction histogram constructed from pixel values and local directional features. In addition to presenting a fast recursive method for REMT, we propose the Rényi entropic artificial bee colony multilevel thresholding (REABCMT) method to quickly find the optimal threshold values. In order to demonstrate the efficacy of REABCMT, three versions of this method are compared in terms of computation time and optimal threshold values. In addition, the segmentation performance of REABCMT is also evaluated by comparing it with two other methods to show its effectiveness. Moreover, in order to evaluate the efficiency and stability of using the ABC algorithm in the search for threshold values, genetic algorithm (GA) and particle swarm optimization (PSO), two common optimization algorithms, are also compared with it.