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.

中文翻译：

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通过拓扑持久性进行3D微结构分割

层析成像是一种广泛用于分析三维（3D）微观结构的工具。然而，由于构成材料产生相似的灰度值，因此分析面临困难。有时，这会促使图像分割过程将像素/体素分配给错误的相（活性物质或孔）。因此，在微结构特性计算中引入了误差。在这项工作中，我们开发了一种基于拓扑持久性的过滤算法，这是一种用于拓扑数据分析的技术。评估过滤算法时面临的一个问题是，真实图像数据通常不具备有关微观结构特征的“地面真实性”信息。对于本研究，我们构建已知地面真实值的合成图像。具体来说，我们比较了相互联系的孔隙曲折度和相分数。实验结果表明，即使相位的灰度值相似，我们的滤波算法也可以显着改善曲折度，使其接近地面真实度。