Post-processing techniques for making reliable measurements from curve-skeletons

Interconnected 3-D networks occur widely in biology and the geometry of such branched networks can be described by curve-skeletons, allowing parameters such as path lengths, path tortuosities and cross-sectional thicknesses to be quantified. However, curve-skeletons are typically sensitive to small scale surface features which may arise from noise in the imaging data. In this paper, new post-processing techniques for curve-skeletons are presented which ensure that measurements of lengths and thicknesses are less sensitive to these small scale surface features. The techniques achieve sub-voxel accuracy and are based on a minimal sphere-network representation in which the object is modelled as a string of minimally overlapping spheres, and as such samples the object on a scale related to the local thickness. A new measure of cross-sectional dimension termed the modal radius is defined and shown to be more robust in comparison with the standard measure (the internal radius), while retaining the desirable feature of capturing the size of structures in terms of a single measure. The techniques are demonstrated by application to trabecular bone and tumour vascular network case studies where the volumetric data was obtained by high resolution computed tomography.