3D Region representation based on run-lengths: operations and efficiency

Abstract This paper discusses a volumetric representation of 3D regions achieved by the generalisation of run-length coding for 2D binary images. Methods for representing 3D regions/objects are discussed. The data structure for recording the runs describing the space occupation of the region is specifically investigated with a performance analysis of the memory requirement. We show that, in the worst case, the run-length description for 3D regions has a better performance on the memory expense than the traditional octree representation. A set of region operations which are basic to many applications are implemented based on the chosen data structure for describing the region. Techniques for achieving an efficient implementation of these operations are described, and detailed algorithms are presented. A quantitative analysis on the computational cost of these operations is also carried out. The representation scheme has been tested in our work on segmentation of 3D grey-level images. With these basic operations, the representation scheme is useful to applications such as computer vision, computer graphics and robotics.