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.

翻译：肿瘤学是分析三个维度(3D)微结构的一个广泛使用的工具。然而,分析面临困难,因为组成材料产生相似的灰度值。有时,这促使图像分割过程将像素/voxel分解到错误的阶段(活性材料或孔隙)。因此,微结构特征计算中引入了错误。在这项工作中,我们开发了一种过滤算法,称为 PerSplat,它基于地形持久性(一种用于地形数据分析的技术)来提高分化质量。在评估过滤算法时遇到的一个问题是,一般真实图像数据没有为微观结构特征配备“地面真相”。对于这项研究,我们制作了已知地面真相值的合成图像。在合成图像中,我们比较了孔线和Minkowski功能(体积和表面区域)与我们PerSplat过滤器和诸如全面变异(TV)和非本地手段(NL- means)等其他方法。此外,在真实的 3D图像中,我们用视觉比较了我们过滤器质量提供的分解结果。