Three-dimensional skeleton and centerline generation based on an approximate minimum distance field

We propose an algorithm for generating 18-connected skeletons and centerlines of 3D binary volume data sets. With of an approximate minimum distance field, we express skeletons as a set of clusters with a set of local maximum paths (LMpaths). Each cluster consists of geometrically adjacent voxels with the same local maximum value. Distinct clusters are connected by all possible LMpaths formed by local maximum voxels snaking along, at most, three fixed directions until they meet other clusters. As a 3D extension, we discuss an LMpath traveling on a straight line before and after reaching a saddle point. We generate the shortest centerline connecting two given points with another similar minimum field over skeletal point sets. The results generated by the algorithms on an experimental data set and colon CT and brain MRI data sets demonstrate their efficiency.