Compression of N-Tree Structures

Objects used in real life are normally three dimensional, although many objects are close to being twoor even one dimensional. In geometry, objects can have any number of dimensions, although we cannot visualize objects in more than three dimensions. An N -tree data structure is a special tree that stores an N -dimensional object. The most common example is a quadtree, a popular structure for storing a two-dimensional object, normally an image. The root of a quadtree corresponds to the entire image. If the image is completely uniform (i.e., all the pixels are the same color) the color is stored in the root, and the root becomes the entire tree. Otherwise, a new level is added to the tree, with four nodes, each corresponding to one quadrant of the image. If a quadrant is uniform, its color is stored in its node and the node becomes a leaf of the quadtree. A nonuniform quadrant adds a new level to the quadtree, with four children nodes that correspond to the four subquadrants of the nonuniform quadrant. This process continues until the subsubquadrants reach the size of a pixel. Figure 1 shows a simple example: