A Multi-Level Image Thresholding Algorithm Based on the Power-Law Distribution

The grayscale histogram plays an important role in image thresholding. However, this kind of global statistical information always involves fluctuations. And the mode of the gray-level distribution is essential to improve segmentation quality. This paper adopts a power-law-like function to fit the grayscale histogram, and a novel multi-thresholding algorithm is proposed. The algorithm generalizes the Gaussian mixture model (GMM) and introduces a non-extensive parameter q to flexibly adapt to the segmentation requirements. Experimental results show that, at threshold numbers of 3, 4, and 5, the proposed algorithm achieves higher PSNR (peak signal-to-noise ratio) on CT images compared with the Kapur algorithm, the Tsallis entropy algorithm, and the self-adaptive Tsallis entropy algorithm (STEA). For images from the same sequence, the optimal q values converge within a narrow range, demonstrating excellent consistency and stability of the proposed algorithm. Furthermore, in terms of the PSNR, SSIM (Structural Similarity Index), FSIM (Feature Similarity Index), and MHD (Modified Hausdorff distance) metrics, the proposed algorithm outperforms the GMM on most CT images, validating its broad applicability to images presenting long-range correlations and heavy-tailed grayscale distributions.