This dissertation deals with the problem of manipulating and storing an image using quadtrees. A quadtree is a tree in which each node has four ordered children or is a leaf. It can be used to represent an image via hierarchical decomposition. The image is broken into four regions. A region can be a solid color (homogeneous) or a mixture of colors (heterogeneous). If a region is heterogeneous it is broken into four subregions, and the process continues recursively until all subregions are homogeneous. The traditional quadtree suffers from dependence on the underlying grid. The grid coordinate system is implicit, and therefore fixed. The fixed coordinate system implies a rigid tree. A rigid tree cannot be translated, scaled, or rotated. Instead, a new tree must be built which is the result of one of these transformations. This dissertation introduces the independent quadtree. The independent quadtree is free of any underlying coordinate system. The tree is no longer rigid and can be easily translated, scaled, or rotated. Algorithms to perform these operations axe presented. The translation and rotation algorithms take constant time. The scaling algorithm has linear time in the number nodes in the tree. The disadvantage of independent quadtrees is …