Title :
Morse theory and persistent homology for topological analysis of 3D images of complex materials
Author :
Delgado-Friedrichs, Olaf ; Robins, Vanessa ; Sheppard, Adrian
Author_Institution :
Dept. of Appl. Math., Australian Nat. Univ., Canberra, ACT, Australia
Abstract :
We develop topologically accurate and compatible definitions for the skeleton and watershed segmentation of a 3D digital object that are computed by a single algorithm. These definitions are based on a discrete gradient vector field derived from a signed distance transform. This gradient vector field is amenable to topological analysis and simplification via For-man´s discrete Morse theory and provides a filtration that can be used as input to persistent homology algorithms. Efficient implementations allow us to process large-scale x-ray micro-CT data of rock cores and other materials.
Keywords :
computerised tomography; filtering theory; image segmentation; materials science computing; transforms; 3D digital object; Forman discrete Morse theory; X-ray micro-CT data processing; computerised tomography; discrete gradient vector field; filtration; persistent homology algorithm; signed distance transform; topological 3D image analysis; topological analysis; watershed segmentation; Bridges; Materials; Skeleton; Three-dimensional displays; Topology; Transforms; Vectors; Discrete Morse theory; Skeletonisation; Topological data analysis; Watershed transform;
Conference_Titel :
Image Processing (ICIP), 2014 IEEE International Conference on
Conference_Location :
Paris
DOI :
10.1109/ICIP.2014.7025987
