Surfaces generated by Additive Manufacturing or laser texturing can involve the solidification of droplets of liquid, which can give rise to overhanging features on the solidified surface. Overhanging features add a layer of complexity to the surface topography and are undetectable by standard surface roughness measurement techniques such as profilometry. Such features are important because they can have a considerable effect on surface properties such as wettability. New techniques and algorithms are therefore required to analyse and quantify convoluted surfaces with overhanging (re-entrant) features. Earlier work by the authors introduced the concept of using X-ray micro-computed tomography (Micro-CT) to identify the directions of vectors normal to the surface at any point and thus indicate the presence or absence of overhanging features. This paper divides overhanging features into two types; simple and compound, and introduces new, size independent, analysis techniques which measure what proportion of each type is on the surface. Another extension of the analysis is the comparison of surface profiles taken in different directions in order to identify any surface roughness anisotropies.