Dynamic Atomic Column Detection in Transmission Electron Microscopy Videos via Ridge Estimation

Ridge detection is a classical tool to extract curvilinear features in image processing. As such, it has great promise in applications to material science problems; specifically, for trend filtering relatively stable atom-shaped objects in image sequences, such as Transmission Electron Microscopy (TEM) videos. Standard analysis of TEM videos is limited to frame-by-frame object recognition. We instead harness temporal correlation across frames through simultaneous analysis of long image sequences, specified as a spatio-temporal image tensor. We define new ridge detection algorithms to non-parametrically estimate explicit trajectories of atomic-level object locations as a continuous function of time. Our approach is specially tailored to handle temporal analysis of objects that seemingly stochastically disappear and subsequently reappear throughout a sequence. We demonstrate that the proposed method is highly effective and efficient in simulation scenarios, and delivers notable performance improvements in TEM experiments compared to other material science benchmarks.

Detection and hypothesis testing of features in extremely noisy image series using topological data analysis, with applications to nanoparticle videos

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$\unicode{8212}$including the novel ALPS statistic$\unicode{8212}$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.