Asymmetric parallel 3D thinning scheme and algorithms based on isthmuses

Critical kernels constitute a general framework settled in the context of abstract complexes for the study of parallel thinning in any dimension. We take advantage of the properties of this framework, to propose a generic thinning scheme for obtaining “thin” skeletons from objects made of voxels. From this scheme, we derive algorithms that produce curve or surface skeletons, based on the notion of 1D or 2D isthmus. We compare our new curve thinning algorithm with all the published algorithms of the same kind, based on quantitative criteria. Our experiments show that our algorithm largely outperforms the other ones with respect to noise sensitivity. Furthermore, we show how to slightly modify our algorithms to include a filtering parameter that controls effectively the pruning of skeletons, based on the notion of isthmus persistence.