Normalized quadtrees with respect to translations

Abstract

Quadtrees offer a compact and hierarchical representation of an image. However, the location of an image segment on the coordinate grid and the grid size itself affect the quadtree representation, making comparison of image segments difficult. To alleviate this difficulty, we propose the concept of a normalized quadtree to represent a given image segment in a unique and optimal way over the class of all translations. An O(s²log₂s) algorithm is presented for obtaining normalized quadtrees, where s is the length of the grid.