We propose a flexible approach for the detection of features in images with ultra low signal-to-noise ratio using cubical persistent homology. Our main application is in the detection of atomic columns and other features in transmission electron microscopy (TEM) images. Cubical persistent homology is used to identify local minima in subregions in the frames of nanoparticle videos, which are hypothesized to correspond to relevant atomic features. We compare the performance of our algorithm to other employed methods for the detection of columns and their intensity. Additionally, Monte Carlo goodness-of-fit testing using real-valued summaries of persistence diagrams -- including the novel ALPS statistic -- derived from smoothed images (generated from pixels residing in the vacuum region of an image) is developed and employed to identify whether or not the proposed atomic features generated by our algorithm are due to noise. Using these summaries derived from the generated persistence diagrams, one can produce univariate time series for the nanoparticle videos, thus providing a means for assessing fluxional behavior. A guarantee on the false discovery rate for multiple Monte Carlo testing of identical hypotheses is also established.
翻译:我们建议采用一种灵活的方法,用单方持久性同族体探测信号到噪音比率极低的图像中的特征。我们的主要应用是探测原子柱和传输电子显微镜图像中的其他特征。阴性持久性同族体用于在纳米粒子视频框中识别各分区域的本地微型,这些视频假设与相关原子特征相对应。我们将我们的算法的性能与用于探测柱子及其强度的其他方法进行比较。此外,利用真实估价的持久性图表摘要 -- -- 包括新的ALPS统计数据 -- -- 进行的蒙特卡洛最佳测试,开发并使用光滑图像(来自位于图像真空区域的像素生成的),以确定我们算法产生的拟议原子特征是否因噪音而产生。使用从生成的耐久性图中得出的这些摘要,可以产生纳米粒子视频的单向时间序列,从而提供一种评估通性行为的手段。还建立了对蒙卡洛对相同假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假假