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The distilled Vietoris Rips filtration for persistent homology and a new memory efficient algorithm
Musashi Ayrton Koyama, Vanessa Robins, Katharine Turner
The long computational time and large memory requirements for computing Vietoris Rips persistent homology from point clouds remains a significant deterrent to its application to bi…
Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform
Nicholas Bermingham, Vanessa Robins, Katharine Turner
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists an…
The Extended Persistent Homology Transform of manifolds with boundary
Katharine Turner, Vanessa Robins, James Morgan
The Extended Persistent Homology Transform (XPHT) is a topological transform which takes as input a shape embedded in Euclidean space, and to each unit vector assigns the extended…