Journal article
Feature Detection and Hypothesis Testing for Extremely Noisy Nanoparticle Images using Topological Data Analysis
Technometrics, Vol.65(4), pp.590-603
2023
DOI: 10.1080/00401706.2023.2203744
Abstract
We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra-low signal-to-noise ratio using cubical persistent homology. Our main application is in the identification of atomic columns and other features in Transmission Electron Microscopy (TEM). Cubical persistent homology is used to identify local minima and their size 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 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.
Details
- Title: Subtitle
- Feature Detection and Hypothesis Testing for Extremely Noisy Nanoparticle Images using Topological Data Analysis
- Creators
- Andrew M. Thomas - Cornell UniversityPeter A. Crozier - School for Engineering of Matter, Transport and Energy, ASUYuchen Xu - Cornell UniversityDavid S. Matteson - Cornell University
- Resource Type
- Journal article
- Publication Details
- Technometrics, Vol.65(4), pp.590-603
- Publisher
- Taylor & Francis
- DOI
- 10.1080/00401706.2023.2203744
- ISSN
- 0040-1706
- eISSN
- 1537-2723
- Grant note
- DOI: 10.13039/100000001, name: National Science Foundation; DOI: 10.13039/501100000930, name: NSF, award: OAC-1940124, CCF-1934985, DMS-2114143, CBET-1604971, OAC-1940263
- Language
- English
- Electronic publication date
- 06/01/2023
- Date published
- 2023
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984446261202771
Metrics
11 Record Views