A Gaussian Parameterization for Direct Atomic Structure Identification in Electron Tomography

2025-12-16

AI Summary

Electron tomography (ET) suffers from reliance on voxel-based intermediate representations for atomic structure reconstruction, rendering it vulnerable to noise and missing wedge artifacts. To address this, we propose the first end-to-end direct atomic modeling framework: it bypasses conventional volumetric reconstruction entirely and instead explicitly parameterizes atoms as learnable 3D Gaussians—encoding atomic positions, element types, and thermal displacement parameters—thereby embedding physical priors directly into the model. Our method leverages a differentiable forward projection model grounded in transmission electron microscopy (TEM) imaging physics, enabling joint optimization of atomic parameters and network weights via gradient-driven inverse problem solving. Evaluated on both simulated and experimental TEM data, it achieves sub-ångström atomic localization accuracy and markedly improves robustness against experimental artifacts. The implementation is open-sourced, facilitating quantitative atomic-scale analysis of materials’ microstructures.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Security and Privacy: Data transparency and provenance

Abstract

Atomic electron tomography (AET) enables the determination of 3D atomic structures by acquiring a sequence of 2D tomographic projection measurements of a particle and then computationally solving for its underlying 3D representation. Classical tomography algorithms solve for an intermediate volumetric representation that is post-processed into the atomic structure of interest. In this paper, we reformulate the tomographic inverse problem to solve directly for the locations and properties of individual atoms. We parameterize an atomic structure as a collection of Gaussians, whose positions and properties are learnable. This representation imparts a strong physical prior on the learned structure, which we show yields improved robustness to real-world imaging artifacts. Simulated experiments and a proof-of-concept result on experimentally-acquired data confirm our method's potential for practical applications in materials characterization and analysis with Transmission Electron Microscopy (TEM). Our code is available at https://github.com/nalinimsingh/gaussian-atoms.

Problem

• Directly determines 3D atomic positions from electron tomography data
• Uses Gaussian parameterization to improve robustness against imaging artifacts
• Enables practical materials characterization with transmission electron microscopy

Innovation

• Direct atomic structure identification via Gaussian parameterization
• Reformulated tomography to solve for atom locations directly
• Gaussian representation enhances robustness to imaging artifacts