Decomposition of 3D Binary Objects into Rectangular Blocks

In this paper we propose a novel algorithm for a decomposition of 3D binary shapes to rectangular blocks. The aim is to minimize the number of blocks. Theoretically optimal brute-force algorithm is known to be NP-hard and practically infeasible. We introduce its polynomial sub-optimal approximation, which transforms the decomposition problem onto a graph-theoretical problem. We show by extensive experiments that the proposed method outperforms the the octree decomposition in terms of the number of blocks on statistically significant level. We also discuss potential applications of the method in image processing.