  Tomography is a widely used tool for analyzing microstructures in three
dimensions (3D). The analysis, however, faces difficulty because the
constituent materials produce similar grey-scale values. Sometimes, this
prompts the image segmentation process to assign a pixel/voxel to the wrong
phase (active material or pore). Consequently, errors are introduced in the
microstructure characteristics calculation. In this work we develop a filtering
algorithm based on topological persistence, a technique used in topological
data analysis. One problem faced when evaluating filtering algorithms is that
real image data in general are not equipped with the 'ground truth' information
about the microstructure characteristics. For this study, we construct
synthetic images for which the ground truth values are known. Specifically, we
compare interconnected pore tortuosity and phase fraction. Experimental results
show that our filtering algorithm provides a significant improvement in
reproducing tortuosity close to the ground truth, even when the grey-scale
values of the phases are similar.
