11 citations · 23 across the 13 of their papers we have counts for
9 papers · 1 filter
Which Vertical Graphs are Non VPHT Reconstructible?
Jette Gutzeit, Kalani Kistler, Tim Ophelders +1
The verbose persistent homology transform (VPHT) is a topological summary of shapes in Euclidean space. Assuming general position, the VPHT is injective, meaning shapes can be reco…
Sweeping Orders for Simplicial Complex Reconstruction
Tim Ophelders, Anna Schenfisch
Standard sweep algorithms require an order of discrete points in Euclidean space, and rely on the property that, at a given point, all points in the halfspace below come earlier in…
How Small Can Faithful Sets Be? Ordering Topological Descriptors
Brittany Terese Fasy, David L. Millman, Anna Schenfisch
Recent developments in shape reconstruction and comparison call for the use of many different (topological) descriptor types, such as persistence diagrams and Euler characteristic…
Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams
Brittany Terese Fasy, Samuel Micka, David L. Millman +2
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in , the (augmented)…
Catching Polygons
Bradley McCoy, Eli Quist, Anna Schenfisch
Consider an arrangement of lines intersecting the unit square. There is some minimum scaling factor so that any placement of a rectangle with aspect ratio with $p\…
A Faithful Discretization of Verbose Directional Transforms
Brittany Terese Fasy, Samuel Micka, David L. Millman +2
The persistent homology transform, Betti function transform, and Euler characteristic transform represent a shape with a multiset of persistence diagrams, Betti functions, or Euler…
Reconstructing Embedded Graphs from Persistence Diagrams
Robin Lynne Belton, Brittany Terese Fasy, Rostik Mertz +6
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides impor…
Challenges in Reconstructing Shapes from Euler Characteristic Curves
Brittany Terese Fasy, Samuel Micka, David L. Millman +2
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries…
Learning Simplicial Complexes from Persistence Diagrams
Robin Lynne Belton, Brittany Terese Fasy, Rostik Mertz +6
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at…