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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.
The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is introduced. We study how to obtain a persistence partial matching $mathcal{G}_f$, and a partial matching $mathcal{M}_f$, induced by a
Many physical systems can be modeled as large sets of domains glued together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet a
The classical persistence algorithm virtually computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological
Zirconium based alloys have been irradiated with 11 and 15 MeV proton and 116 MeV oxygen ions at different doses. The changes in the microstructure have been studied for the ion irradiated alloys as a function of dose using X-Ray Diffraction Line Pro
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris-Rips, Cech and witness complexes) built on top of precompact spaces. Using recent developments in the theory of topological persistence