Delgado-Friedrichs, OlafRobins, VanessaSheppard, Adrian2015-03-112015-03-110162-8828http://hdl.handle.net/1885/12873We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons and partitions of grayscale digital images. We model a grayscale image as a cubical complex with a real-valued function defined on its vertices (the voxel values). This function is extended to a discrete gradient vector field using the algorithm presented in Robins, Wood, Sheppard TPAMI 33:1646 (2011). In the current paper we define basins (the building blocks of a partition) and segments of the skeleton using the stable and unstable sets associated with critical cells. The natural connection between Morse theory and homology allows us to prove the topological validity of these constructions; for example, that the skeleton is homotopic to the initial object. We simplify the basins and skeletons via Morse-theoretic cancellation of critical cells in the discrete gradient vector field using a strategy informed by persistent homology. Simple working Python code for our algorithms for efficient vector field traversal is included. Example data are taken from micro-CT images of porous materials, an application area where accurate topological models of pore connectivity are vital for fluid-flow modelling.http://www.sherpa.ac.uk/romeo/issn/0162-8828/..."If funding rules apply authors may post Author's post-print version in funder's designated repository. Author's Post-print - Publisher copyright and source must be acknowledged with citation (see set statement below). Author's Post-print - Must link to publisher version with DOI. Publisher's version/PDF cannot be used." from SHERPA/RoMEO site (as at 27/03/15) © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Curve skeletonsurface skeletonmedial axis transformwatershed transformdiscrete Morse theorypersistent homology2015-02-1310.1109/TPAMI.2014.23461722016-06-14