The Impact of Changes in Resolution on the Persistent Homology of Images

Teresa Heiss; Sarah Tymochko; Brittany Story; Adélie Garin; Hoa Bui; Bea Bleile; Vanessa Robins

doi:10.1109/BigData52589.2021.9671483

The Impact of Changes in Resolution on the Persistent Homology of Images

Teresa Heiss, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea Bleile, Vanessa Robins

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.

Original language	English
Title of host publication	Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021
Editors	Yixin Chen, Heiko Ludwig, Yicheng Tu, Usama Fayyad, Xingquan Zhu, Xiaohua Tony Hu, Suren Byna, Xiong Liu, Jianping Zhang, Shirui Pan, Vagelis Papalexakis, Jianwu Wang, Alfredo Cuzzocrea, Carlos Ordonez
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3824-3834
Number of pages	11
ISBN (Electronic)	9781665439022
DOIs	https://doi.org/10.1109/BigData52589.2021.9671483
Publication status	Published - 2021
Event	2021 IEEE International Conference on Big Data, Big Data 2021 - Virtual, Online, United States Duration: 15 Dec 2021 → 18 Dec 2021

Publication series

Name	Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021

Conference

Conference	2021 IEEE International Conference on Big Data, Big Data 2021
Country/Territory	United States
City	Virtual, Online
Period	15/12/21 → 18/12/21

Access to Document

10.1109/BigData52589.2021.9671483

Cite this

Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., & Robins, V. (2021). The Impact of Changes in Resolution on the Persistent Homology of Images. In Y. Chen, H. Ludwig, Y. Tu, U. Fayyad, X. Zhu, X. T. Hu, S. Byna, X. Liu, J. Zhang, S. Pan, V. Papalexakis, J. Wang, A. Cuzzocrea, & C. Ordonez (Eds.), Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021 (pp. 3824-3834). (Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/BigData52589.2021.9671483

Heiss, Teresa ; Tymochko, Sarah ; Story, Brittany et al. / The Impact of Changes in Resolution on the Persistent Homology of Images. Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021. editor / Yixin Chen ; Heiko Ludwig ; Yicheng Tu ; Usama Fayyad ; Xingquan Zhu ; Xiaohua Tony Hu ; Suren Byna ; Xiong Liu ; Jianping Zhang ; Shirui Pan ; Vagelis Papalexakis ; Jianwu Wang ; Alfredo Cuzzocrea ; Carlos Ordonez. Institute of Electrical and Electronics Engineers Inc., 2021. pp. 3824-3834 (Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021).

@inproceedings{6e8880be63104a7193f2213f3e366015,

title = "The Impact of Changes in Resolution on the Persistent Homology of Images",

abstract = "Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.",

keywords = "image processing, image resolution, persistent homology",

author = "Teresa Heiss and Sarah Tymochko and Brittany Story and Ad{\'e}lie Garin and Hoa Bui and Bea Bleile and Vanessa Robins",

note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 2021 IEEE International Conference on Big Data, Big Data 2021 ; Conference date: 15-12-2021 Through 18-12-2021",

year = "2021",

doi = "10.1109/BigData52589.2021.9671483",

language = "English",

series = "Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3824--3834",

editor = "Yixin Chen and Heiko Ludwig and Yicheng Tu and Usama Fayyad and Xingquan Zhu and Hu, {Xiaohua Tony} and Suren Byna and Xiong Liu and Jianping Zhang and Shirui Pan and Vagelis Papalexakis and Jianwu Wang and Alfredo Cuzzocrea and Carlos Ordonez",

booktitle = "Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021",

address = "United States",

}

Heiss, T, Tymochko, S, Story, B, Garin, A, Bui, H, Bleile, B & Robins, V 2021, The Impact of Changes in Resolution on the Persistent Homology of Images. in Y Chen, H Ludwig, Y Tu, U Fayyad, X Zhu, XT Hu, S Byna, X Liu, J Zhang, S Pan, V Papalexakis, J Wang, A Cuzzocrea & C Ordonez (eds), Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021. Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021, Institute of Electrical and Electronics Engineers Inc., pp. 3824-3834, 2021 IEEE International Conference on Big Data, Big Data 2021, Virtual, Online, United States, 15/12/21. https://doi.org/10.1109/BigData52589.2021.9671483

The Impact of Changes in Resolution on the Persistent Homology of Images. / Heiss, Teresa; Tymochko, Sarah; Story, Brittany et al.
Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021. ed. / Yixin Chen; Heiko Ludwig; Yicheng Tu; Usama Fayyad; Xingquan Zhu; Xiaohua Tony Hu; Suren Byna; Xiong Liu; Jianping Zhang; Shirui Pan; Vagelis Papalexakis; Jianwu Wang; Alfredo Cuzzocrea; Carlos Ordonez. Institute of Electrical and Electronics Engineers Inc., 2021. p. 3824-3834 (Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - The Impact of Changes in Resolution on the Persistent Homology of Images

AU - Heiss, Teresa

AU - Tymochko, Sarah

AU - Story, Brittany

AU - Garin, Adélie

AU - Bui, Hoa

AU - Bleile, Bea

AU - Robins, Vanessa

PY - 2021

Y1 - 2021

N2 - Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.

AB - Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.

KW - image processing

KW - image resolution

KW - persistent homology

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DO - 10.1109/BigData52589.2021.9671483

M3 - Conference contribution

AN - SCOPUS:85125316096

T3 - Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021

SP - 3824

EP - 3834

BT - Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021

A2 - Chen, Yixin

A2 - Ludwig, Heiko

A2 - Tu, Yicheng

A2 - Fayyad, Usama

A2 - Zhu, Xingquan

A2 - Hu, Xiaohua Tony

A2 - Byna, Suren

A2 - Liu, Xiong

A2 - Zhang, Jianping

A2 - Pan, Shirui

A2 - Papalexakis, Vagelis

A2 - Wang, Jianwu

A2 - Cuzzocrea, Alfredo

A2 - Ordonez, Carlos

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 IEEE International Conference on Big Data, Big Data 2021

Y2 - 15 December 2021 through 18 December 2021

ER -

Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B et al. The Impact of Changes in Resolution on the Persistent Homology of Images. In Chen Y, Ludwig H, Tu Y, Fayyad U, Zhu X, Hu XT, Byna S, Liu X, Zhang J, Pan S, Papalexakis V, Wang J, Cuzzocrea A, Ordonez C, editors, Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021. Institute of Electrical and Electronics Engineers Inc. 2021. p. 3824-3834. (Proceedings - 2021 IEEE International Conference on Big Data, Big Data 2021). doi: 10.1109/BigData52589.2021.9671483

The Impact of Changes in Resolution on the Persistent Homology of Images

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