Octrees and their applications in image processing

It is shown how the octree and its digital representation, octcodes, can be used as the primary data structure in a number of applications in image processing. The authors consider only raster data and assume that no voxel can contain data having more than one color. Algorithms are presented only in a descriptive manner. The octree is a hierarchical representation of a 2ⁿ×2ⁿ×2ⁿ (n⩾1) array of unit cubes or voxels, each of which has value BLACK or WHITE. The subset of BLACK voxels constitutes the object and the subset of WHITE voxels constitutes the surrounding space. The primary advantage of the octree is that it can be used to describe the successive partitions of a 2ⁿ×2ⁿ×2ⁿ array in octants, to separate an object from its surrounding space. Using the principle of recursive decomposition, the authors show how the octree can be used as the primary data structure in a number of 3-D applications in image processing. These applications include object representation; union, intersection, and difference of objects; transformations; adjacency; and windowing and clipping