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 defined 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 effectiveness 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.