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

TL;DR

This work tackles the challenge of tracking atomic columns in high-noise TEM videos by proposing a non-parametric, spatio-temporal ridge estimation framework that leverages temporal correlations to recover continuous trajectories. The method combines intra-frame ridge indicators with an inter-frame continuity penalty to score and assemble candidate ridge points across frames, followed by a kernel-based non-parametric curve connection to yield a smooth trajectory over time, along with uncertainty quantification. Through simulations and synthetic TEM experiments, the approach demonstrates improved accuracy and robustness relative to framewise benchmarks, including scenarios with disappearing and reappearing columns. The framework offers practical value for in situ materials analysis by enabling reliable, continuous tracking of atomic-scale features under challenging imaging conditions.

Abstract

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.

Figures (14)

• Figure 1: The sketch of a time-resolved in situ TEM video of a $\hbox{CeO}_2$ nanoparticle with temporal resolution 2.5 milliseconds. Here, the $x$ and $y$ axes identify the spatial coordinates within single TEM image frames, and the $t$ axis represents the dimension of time. Every single frame visualizes the physical nanoparticles' model as the gray-scaled projection image, and the whiter regions are the places where atoms are stacked to form atomic columns perpendicular to the page. A zoomed view for one of the atomic columns is provided as \ref{['fig:blob_ridge']}.
• Figure 2: The illustration of a generalized ridge curve $\gamma \subset \mathbb{R}^3$ as a trajectory function of time $t$ for a selected atomic column after negating the TEM video. The negation is supported as in \ref{['rem:def']}. In the example sequence, the atomic column experiences various dynamics such as shrinking and expanding radius, decreasing and increasing contrasts, and total degeneration to a single point in the middle of the series. In addition, the outer contour of the atomic column forms a tube-shaped object that stretches temporally.
• Figure 3: The projected behaviors of the mapping $f$ at a ridge point $p \in \gamma$ along the axes of a local coordinate system. Here the basis of the new coordinate system is formed by the set of orthonormal Hessian eigenvectors $\{v_1(p), v_2(p), v_3(p)\}$.
• Figure 4: Illustration of \ref{['def:rough']} for the interpolation and the roughness penalization.
• Figure 5: Illustration of \ref{['def:score']} for the forward and backward metrics.

Theorems & Definitions (30)

• Definition 1
• Remark 1
• Remark 2
• Definition 2
• Remark 3
• Remark 4
• Definition 3
• Remark 5
• Proposition 1
• Remark 6