Skip navigation
Skip navigation

Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images

Robins, Vanessa; Wood, Peter J; Sheppard, Adrian

Description

We present an algorithm for determining the Morse complex of a two or three-dimensional grayscale digital image. Each cell in the Morse complex corresponds to a topological change in the level sets (i.e., a critical point) of the grayscale image. Since more than one critical point may be associated with a single image voxel, we model digital images by cubical complexes. A new homotopic algorithm is used to construct a discrete Morse function on the cubical complex that agrees with the digital...[Show more]

dc.contributor.authorRobins, Vanessa
dc.contributor.authorWood, Peter J
dc.contributor.authorSheppard, Adrian
dc.date.accessioned2015-12-10T22:54:42Z
dc.identifier.issn0162-8828
dc.identifier.urihttp://hdl.handle.net/1885/59753
dc.description.abstractWe present an algorithm for determining the Morse complex of a two or three-dimensional grayscale digital image. Each cell in the Morse complex corresponds to a topological change in the level sets (i.e., a critical point) of the grayscale image. Since more than one critical point may be associated with a single image voxel, we model digital images by cubical complexes. A new homotopic algorithm is used to construct a discrete Morse function on the cubical complex that agrees with the digital image and has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets. We make use of discrete Morse theory and simple homotopy theory to prove correctness of this algorithm. The resulting Morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)
dc.sourceIEEE Transactions on Pattern Analysis and Machine Intelligence
dc.subjectKeywords: Computational topology; Critical cells; Critical points; Cubical complex; Digital image; Digital topology; Discrete Morse theory; Gray scale; Gray-scale images; Homotopic; Homotopy theory; Level Set; Morse functions; Persistent homology; Single images; To computational topology; digital topology; Discrete Morse theory; persistent homology
dc.titleTheory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume33
dc.date.issued2011
local.identifier.absfor020406 - Surfaces and Structural Properties of Condensed Matter
local.identifier.absfor020402 - Condensed Matter Imaging
local.identifier.absfor080106 - Image Processing
local.identifier.ariespublicationu9210271xPUB506
local.type.statusPublished Version
local.contributor.affiliationRobins, Vanessa, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationWood, Peter J, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationSheppard, Adrian, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.issue8
local.bibliographicCitation.startpage1646
local.bibliographicCitation.lastpage1658
local.identifier.doi10.1109/TPAMI.2011.95
dc.date.updated2016-02-24T11:56:15Z
local.identifier.scopusID2-s2.0-79959524693
local.identifier.thomsonID000291807200012
CollectionsANU Research Publications

Download

File Description SizeFormat Image
01_Robins_Theory_and_Algorithms_for_2011.pdf1.87 MBAdobe PDF    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  19 May 2020/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator