  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 called PerSplat based on topological persistence (a
technique used in topological data analysis) to improve segmentation quality.
One problem faced when evaluating filtering algorithms is that real image data
in general are not equipped with the `ground truth' for the microstructure
characteristics. For this study, we construct synthetic images for which the
ground-truth values are known. On the synthetic images, we compare the pore
tortuosity and Minkowski functionals (volume and surface area) computed with
our PerSplat filter and other methods such as total variation (TV) and
non-local means (NL-means). Moreover, on a real 3D image, we visually compare
the segmentation results provided by our filter against TV and NL-means. The
experimental results indicate that PerSplat provides a significant improvement
in segmentation quality.
