Image thresholding by variational minimax optimization

Abstract

In this paper we introduce an adaptive image thresholding technique via minimax optimization of a novel energy functional that consists of a non-linear convex combination of an edge sensitive data fidelity term and a regularization term. While the proposed data fidelity term requires the threshold surface to intersect the image surface only at places with large image gradient magnitude, the regularization term enforces smoothness in the threshold surface. To the best of our knowledge, all the previously proposed energy functional-based adaptive image thresholding algorithms rely on manually set weighting parameters to achieve a balance between the data fidelity and the regularization terms. In contrast, we use minimax principle to automatically find this weighting parameter value, as well as the threshold surface. Our conscious choice of the energy functional permits a variational formulation within the minimax principle leading to a globally optimum solution. The proposed variational minimax optimization is carried out by an iterative gradient descent with exact line search technique that we experimentally demonstrate to be computationally far more attractive than the Fibonacci search applied to find the minimax solution. Our method shows promising results to preserve edge/texture structures in different benchmark images over other competing methods. We also demonstrate the efficacy of the proposed method for delineating lung boundaries from magnetic resonance imagery (MRI).