CT colonography is an emerging technique for colorectal cancer screening. This technique facilitates noninvasive imaging of the colon interior by generating virtual reality models of the colon lumen. Manual navigation through these models is a slow and tedious process. It is possible to automate navigation by calculating the centreline of the colon lumen. There are numerous well documented approaches for centreline calculation. Many of these techniques have been developed as alternatives to 3D topological thinning which has been discounted by others due to its computationally intensive nature. This paper describes a fully automated, optimised version of 3D topological thinning that has been specifically developed for calculating the centreline of the human colon.