Fast and accurate lacunarity calculation for large 3D micro-CT datasets

Microcomputed-tomography (micro-CT) is a 3D imaging method capable of revealing the complete inner structure of materials. Besides imaging, micro-CT also provides quantitative information about numerous structural features including lacunarity, which describes the heterogeneity of samples quantitatively. Theoretically, lacunarity is easily calculated using the gliding box method. However, when implemented in 3D, the computational costs of this method increase enormously, thus preventing its widespread use for large micro-CT datasets. Here we suggest a faster alternative method, based on the fixed-grid algorithm, which offers a viable alternative and renders 3D lacunarity calculations on micro-CT data feasible. Since a possible shortcoming of this alternative is that its reduced data could result in an inferior description of the real spatial heterogeneity of the structures, the two methods are compared concerning the accuracy, computational time, and applicability in materials science. The calculations are carried out on real 3D micro-CT datasets. Our implementation of the fixed-grid method can approximate gliding box lacunarity values rapidly and accurately, especially for large datasets of homogeneous structures. Therefore, we propose adding the fixed-grid method lacunarity calculation to the routine micro-CT analysis toolbox. Our image acquisition platform-independent software (Lac3D) to carry out this calculation is made freely accessible here.