18 citations · 45 across the 10 of their papers we have counts for
10 papers
Identifying cobordisms using kernel persistence
Yossi Bokor Bleile, Lisbeth Fajstrup, Teresa Heiss +2
Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered comple…
Merge Trees of Periodic Filtrations
Herbert Edelsbrunner, Teresa Heiss
Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are…
Flips in Two-dimensional Hypertriangulations
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2
We study flips in hypertriangulations of planar points sets. Here a level- hypertriangulation of points in the planes is a subdivision induced by the projection of a -hyp…
On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2
For a locally finite set in , the order- Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dens…
Brillouin Zones of Integer Lattices and Their Perturbations
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +3
For a locally finite set, , the -th Brillouin zone of is the region of points for which is the -th smallest…
The Impact of Changes in Resolution on the Persistent Homology of Images
Teresa Heiss, Sarah Tymochko, Brittany Story +4
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging.…
The Density Fingerprint of a Periodic Point Set
Herbert Edelsbrunner, Teresa Heiss, Vitaliy Kurlin +2
Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functions that facilitates the efficient search for new materials and material properties…
The Persistent Homology of Dual Digital Image Constructions
Bea Bleile, Adélie Garin, Teresa Heiss +2
To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructio…
Duality in Persistent Homology of Images
Adélie Garin, Teresa Heiss, Kelly Maggs +2
We derive the relationship between the persistent homology barcodes of two dual filtered CW complexes. Applied to greyscale digital images, we obtain an algorithm to convert barcod…
Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images
Teresa Heiss, Hubert Wagner
We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used…