Fast connected-component labelling in three-dimensional binary images based on iterative recursion

We propose two new methods to label connected components based on iterative recursion: one directly labels an original binary image while the other labels the boundary voxels followed by one-pass labelling of non-boundary object voxels. The novelty of the proposed methods is a fast labelling of large datasets without stack overflow and a flexible trade-off between speed and memory. For each iterative recursion: (1) the original volume is scanned in the raster order and an initially unlabelled object voxel v is selected, (2) a sub-volume with a user-defined size is formed around the selected voxel v, (3) within this sub-volume all object voxels 26-connected to v are labelled using iterations; and (4) subsequent iterative recursions are initiated from those border object voxels of the sub-volume that are 26-connected to v. Our experiments show that the time-memory trade-off is that the decrease in the execution time by one-third requires the increase in memory size by 3 orders. This trade-off is controlled by the user by changing the size of the sub-volume. Experiments on large three-dimensional brain phantom datasets (362 × 432 × 362 voxels of 56 MB (megabytes)) show that the proposed methods are three times faster on the average (with the maximum speedup of 10) than the existing iterative methods based on label equivalences with less than 1 MB memory consumption. Moreover, our algorithms are applicable to any dimensional data and are less dependant on the geometric complexity of connected components.