CxCxC: Compressed connected components labeling algorithm

We propose Compressed Connected Components (C x C x C), a new fast algorithm for labeling connected components in binary images making use of compression. We break the given 3D image into non-overlapping 2 x 2 x 2 cube of voxels (2x2 square of pixels for 2D) and encode these binary values as the bits of a single decimal integer. We perform the connected component labeling on the resulting compressed data set. A recursive labeling approach by the use of smart-masks on the encoded decimal values is performed. The output is finally decompressed back to the original size by decimal-to-binary conversion of the cubes to retrieve the connected components in a lossless fashion. We demonstrate the efficacy of such encoding and labeling for large data sets (up to 1392 x 1040 for 2D and 512 x 512 x 336 for 3D). C x C x C reports a speed gain of 4x for 2D and 12x for 3D with memory savings of 75% for 2D and 88% for 3D over conventional (recursive growing of component labels) connected components algorithm. We also compare our method with VTK's "< vtkImageConnectMeasure >" filter and ITK's "< itk::ConnectedComponentlmageFilter >" and find that we outperform both with speed gains of 3x and 6x for 3D. These features make C x C x C highly suitable for medical imaging and multi-media applications where the size of data sets and the number of connected components can be very large.