🍩 Database of Original & Non-Theoretical Uses of Topology
(found 4 matches in 0.001482s)
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Morse Theory and Persistent Homology for Topological Analysis of 3D Images of Complex Materials (2014)
O. Delgado-Friedrichs, V. Robins, A. SheppardAbstract
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. -
Theory and Algorithms for Constructing Discrete Morse Complexes From Grayscale Digital Images (2011)
V. Robins, P. J. Wood, A. P. SheppardAbstract
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 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. -
Topological Persistence for Relating Microstructure and Capillary Fluid Trapping in Sandstones (2019)
A. L. Herring, V. Robins, A. P. SheppardAbstract
Results from a series of two-phase fluid flow experiments in Leopard, Berea, and Bentheimer sandstones are presented. Fluid configurations are characterized using laboratory-based and synchrotron based 3-D X-ray computed tomography. All flow experiments are conducted under capillary-dominated conditions. We conduct geometry-topology analysis via persistent homology and compare this to standard topological and watershed-partition-based pore-network statistics. Metrics identified as predictors of nonwetting fluid trapping are calculated from the different analytical methods and are compared to levels of trapping measured during drainage-imbibition cycles in the experiments. Metrics calculated from pore networks (i.e., pore body-throat aspect ratio and coordination number) and topological analysis (Euler characteristic) do not correlate well with trapping in these samples. In contrast, a new metric derived from the persistent homology analysis, which incorporates counts of topological features as well as their length scale and spatial distribution, correlates very well (R2 = 0.97) to trapping for all systems. This correlation encompasses a wide range of porous media and initial fluid configurations, and also applies to data sets of different imaging and image processing protocols.