# Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms

## TL;DR

This paper introduces a phase-space sketching method for automatic, invariant, and stable analysis of complex microscopic crystal images, enhancing quantitative characterization in materials science.

## Contribution

It presents a novel phase-space sketching technique that encodes crystal images invariant to transformations and extends analysis to complex geometries.

## Key findings

- Invariant representation of crystal images achieved
- Method stable under small deformations
- Extended analysis framework for complex structures

## Abstract

Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of potentially complicated microscopic crystal images, providing feedback to tweak theories and improve synthesis in materials science. As such, an efficient phase-space sketching method is proposed to encode microscopic crystal images in a translation, rotation, illumination, and scale invariant representation, which is also stable with respect to small deformations. Based on the phase-space sketching, we generalize our previous analysis framework for crystal images with simple structures to those with complicated geometry.