Global optimization of wavelet-domain hidden Markov tree for image segmentation

This work presents a global energy minimization method for multiscale image segmentation using convex optimization theory. The construction of energy function is motivated by the intuition that the larger the entropy, the less a priori information one has on the value of the random variables. First, we represent the wavelet-domain hidden Markov tree (WHMT) model of the original image as a structured energy function, which is proved convex in marginal distributions. Next, we derive the maximum lower bound of the energy function through Lagrange dual transform for the purpose of incorporating marginal constraints into optimization. Finally, a modified belief propagation optimization algorithm is used to perform global energy minimization of the dual convex energy function. Experiments on real image segmentation problems demonstrate the superior performance of this new algorithm when compared with nonconvex ones.

► We construct a multiscale energy function which is proved convex in pseudomarginals.
► Global optimal classification likelihoods of the convex energy would be guaranteed.
► We derive maximum lower bound of the convex energy through Lagrange dual transform.
► Marginal constraints are thus incorporated into each step of belief propagation.
► Segmentation experiments reveal the superiority in terms of accuracy and robustness.