In this paper we propose a locally adaptive image threshold technique via variational energy minimization. The novelty of the proposed method is that from an image it automatically computes the weights on the data fidelity and the regularization terms in the energy functional, unlike many other previously proposed variational formulations that require manual input of these weights by laborious trial and error. To achieve the automatic setting of the weighting parameters we propose a non-linear convex combination of the data fidelity and the regularization terms in the energy functional and seek the optimum threshold surface via minimax principle. Our choice of the novel energy functional allows fast computation of the unique minimax solution. As a specific segmentation application, the proposed technique shows promising results when applied to find lung boundary from MR imagery. Illustrative examples are also provided where the proposed method is observed to retain texture information better than other competing methods.