This paper proposes a modified version of freshly developed Equilibrium Optimizer (EO) for segmentation of gray-scale images using multi-level thresholding. Laplace distribution based random walk is utilized to update the concentration of search agents around equilibrium candidates (best solution) towards to attain optimal position (equilibrium state) for achieving better diversification of search space. An opposition based learning (OBL) mechanism is then applied with hybridization of the varying acceleration coefficient to the best solution for accelerating exploitation at a later phase of each iteration. The performance of proposed Opposition-based Laplacian Equilibrium Optimizer (OB-L-EO) is validated using test suites containing benchmark problems of wide varieties of complexities. Various analyses are conducted including Wilcoxon ranksum test for statistical significance, convergence curves and distance between solution before and after applying modification strategies. Finally, the proposed OB-L-EO is employed for image segmentation by utilizing Otsu's interclass variance function to obtain optimum threshold values for image segmentation. The performance of the proposed algorithm is verified by determining mean value of interclass variance and peak signal to noise ratio (PSNR). The obtained results are then compared and analysed with other metaheuristics algorithms to show superiority of proposed OB-L-EO.