Multilevel image thresholding based on Renyi's entropy and golden sinus algorithm II

Abstract

The image thresholding methods consume a lot of time due to computational complexity when the number of threshold levels increases. In order to reduce computation time and improve thresholding performance, we propose a new thresholding method based on the golden sinus algorithm II (GoldSa-II) and Renyi's entropy. GoldSa-II narrows the search space and converges to the targeted optimum point (optimal thresholds) more accurately in a shorter time using the decreasing sine function and the golden ratio. Firstly, a two-dimensional non-local means histogram is constructed and segmentation is carried out based on the gray-level images with various thresholding levels. Performance evaluation is done using 12 different image quality measurement indices (BDE, PRI, GCE, SSIM, FSIM, VOI, RMSE, NAE, PSNR, CC, MD, and AD) using proposed the two-dimensional, non-local means golden sinus algorithm II segmentation method (NLM-GoldSa-II). Experimental results have been performed with 300 images obtained from the Berkeley-Benchmark dataset. The results are compared with six other segmentation methods in terms of computational times, fitness values, and optimal thresholding values. In the segmentation performed with 3-level and 5-level thresholding, it is seen from the studies that 7 out of 12 quality measurement indices give the best results when compared to the other segmentation methods. Improvements in the indicated indices have been achieved by 5.4151% in MD, 33.11% in CC, 0.1011% in RMSE, 0.1618% in FSIM, 0.6180% in VOI, 0.0615% in BDE and 0.4557% in PRI for 3-level thresholding. Improvements in the indicated indices have been achieved by 1.3591% in NAE, 3.2552% in MD, 17.6973% in CC, 0.2176% in RMSE, 0.1939% in SSIM, 0.02551% in FSIM and 1.7236% in BDE for 5-level thresholding. In addition, it has been shown that the proposed method reaches the highest fitness value when compared to other methods, thus achieving the optimal thresholds. Segmentations of sample images from the BSDS300 dataset are illustrated based on the proposed method, plus other existing segmentation methods, with the proposed method producing superior results over the current methods.