Accurate Estimation of Gaussian and Mean Curvature in Volumetric Images

Curvature is a useful low level surface descriptor of wood fibres in {3D} micro-CT images of paper and composite materials. It may for instance be used to differentiate between the outside and the inside (lumen) of wood fibre. Since the image acquisition introduces noise, some kind of smoothing is required to obtain accurate estimates of curvature. However, in these materials, the fibres of interest are frequently both thin and densely packed. In this paper, we show how existing methods fail to accurately capture curvature information under these circumstances. Maintained resolution and smoothing of noise are two competing goals. In some situations, existing methods will even estimate the wrong signs of the principal curvatures. We also present a novel method, which is shown to have better performance in several experiments. This new method will generically produce better curvature estimates for thin objects and objects in close proximity.