Z-Trees: Adaptive Pyramid-Algorithms for Image Segmentation

This paper introduces a direction-sensitive and locally reorientable compact binary tree, called the Z tree, for representing digital images. A rotation operation is de ned on a subset of its node, called square nodes, to spatially reorganize the four grand children of any given square-node. The goal is to adapt the Z tree in order to produce a minimal cutset representation of homogeneous regions. This will enhance a tree-based dynamic programming approach to image segmentation. The tree transformation, tree rotation, and tree inverse transformation, as a sequence { is compactly expressed in the algebraic form of pseudo inverses. Such an expression is conjectured to be universal for segmentation. Experimental results are included to illustrate the e ectiveness of the adaptively orientable trees for image segmentation, including a discussion on the choice of metrics that would warrant a local rotation. Natural extension of this approach to 3-D images, and higher dimensional grids is also outlined.