Irregular Tree-Structured Bayesian Network for image segmentation

Unsupervised image segmentation algorithms rely heavily on a probabilistic smoothing prior to enforce local homogeneity in the segmentation results. The tree-structured prior [1, 2, 3] is one such prior which allows important multi-scale spatial correlations that exist in natural images to be captured. Two main types of tree structure prior have been previously proposed: 1) fixed quadtree structure [1], which suffers from “blockiness” in the segmentation results and 2) flexible tree structure [2, 3] which can adapt its structure to the natural object boundary but at a significant computational cost. This paper presents a novel probabilistic unsupervised image segmentation framework called Irregular Tree-Structured Bayesian Networks (ITSBN) which introduces the notion of irregular tree structure that combines the merits of the two previous approaches. As in [2, 3], more natural object boundaries can be modeled in our framework since a tree is learned for each input image. Our method, however, does not update the adaptive structure at every iteration which drastically reduces the computation required. We derive a time-efficient exact inference algorithm based on a sum-product framework using factor graphs [4]. Furthermore, a novel methodology for the evaluation of unsupervised image segmentation is proposed. By integrating non-parametric density estimation techniques with the traditional precision-recall framework, the proposed method is more robust to boundary inconsistency due to human subjects.