This paper proposed a novel method for global continuous optimization of maximum a posterior(MAP) during wavelet-domain hidden Markov tree-based(WHMT) multiscale information fusion process. We start with calculating the multiscale classification likelihoods of wavelet coefficients by expectation-maximization(EM) algorithm. Energy function is then generated by combining boundary term estimated by classification likelihoods with regional term obtained by both pixel information and approximation coefficients. Through energy minimization through graph cut via convex optimization, objects are segmented accurately from the images in a global optimization sense. A performance measure for tobacco leaf inspection is used to evaluate our algorithm, the localization accuracy of weak boundary by fusing multiscale information via convex optimization is encouraging.