Image segmentation is crucial in image analysis and computer vision applications. Image thresholding, a popular approach due to its simplicity and robustness, becomes less efficient with an increase in thresholds due to an exhaustive search. Evolutionary algorithms like differential evolution (DE) can address this. Generalised Masi entropy (GME) leverages entropic measure (r) to explore additive/non-extensive information for thresholding. However, determining a proper value for r is vital for GME’s performance. This paper proposes a self-adjusting method to find the r value without prior knowledge of histogram distribution. Introducing a new representation compatible with any evolutionary algorithm, the approach retains efficiency without additional function evaluations. Using DE for optimisation, our experiments on benchmark images show significant improvements in the objective function, peak signal-to-noise ratio (PSNR), feature similarity index (FSIM), and structural similarity index (SSIM). This demonstrates the proposed approach’s ability to automatically find the optimal r value and enhance GME-based thresholding efficacy.