A comment on the rank correlation merit function for 2D/3D registration
Michael Figl, Christoph Bloch, Wolfgang Birkfellner · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
Lots of procedures in computer assisted interventions register pre-interventionally generated 3D data sets to the intraoperative situation using fast and simply generated 2D images, e.g. from a C-Arm, a B-mode Ultrasound, etc. Registration is typically done by generating a 2D image out of the 3D data set, comparison to the original 2D image using a planar similarity measure and subsequent optimisation. As these two images can be very different, a lot of different comparison functions are in use. In a recent article Stochastic Rank Correlation, a merit function based on Spearman's rank correlation coefficient was presented. By comparing randomly chosen subsets of the images, the authors wanted to avoid the computational expense of sorting all the points in the image. In the current paper we show that, because of the limited grey level range in medical images, full image rank correlation can be computed almost as fast as Pearson's correlation coefficient. A run time estimation is illustrated with numerical results using a 2D Shepp-Logan phantom at different sizes, and a sample data set of a pig.