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pro vyhledávání: '"Millman, David L."'
Recent developments in shape reconstruction and comparison call for the use of many different (topological) descriptor types, such as persistence diagrams and Euler characteristic functions. We establish a framework to quantitatively compare the stre
Externí odkaz:
http://arxiv.org/abs/2402.13632
Publikováno v:
Proc. 18th Algorithms and Data Structures Symposium. 605-619, 2023
Let $\gamma$ be a generic closed curve in the plane. Samuel Blank, in his 1967 Ph.D. thesis, determined if $\gamma$ is self-overlapping by geometrically constructing a combinatorial word from $\gamma$. More recently, Zipei Nie, in an unpublished manu
Externí odkaz:
http://arxiv.org/abs/2309.02383
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 $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of persistence dia
Externí odkaz:
http://arxiv.org/abs/2212.13206
The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT such that it
Externí odkaz:
http://arxiv.org/abs/1912.12759
Autor:
Belton, Robin Lynne, Fasy, Brittany Terese, Mertz, Rostik, Micka, Samuel, Millman, David L., Salinas, Daniel, Schenfisch, Anna, Schupbach, Jordan, Williams, Lucia
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 important geometric and topological information about a space. Recent work
Externí odkaz:
http://arxiv.org/abs/1912.08913
Autor:
Fasy, Brittany Terese, He, Xiaozhou, Liu, Zhihui, Micka, Samuel, Millman, David L., Zhu, Binhai
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a set of other
Externí odkaz:
http://arxiv.org/abs/1812.11257
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 of shapes and utilized to compute distances. In this abstract, we expl
Externí odkaz:
http://arxiv.org/abs/1811.11337
Autor:
Belton, Robin Lynne, Fasy, Brittany Terese, Mertz, Rostik, Micka, Samuel, Millman, David L., Salinas, Daniel, Schenfisch, Anna, Schupbach, Jordan, Williams, Lucia
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 different scales. Turner, Mukeherjee, and Boyer showed that one can re
Externí odkaz:
http://arxiv.org/abs/1805.10716
Autor:
Belton, Robin Lynne, Fasy, Brittany Terese, Mertz, Rostik, Micka, Samuel, Millman, David L., Salinas, Daniel, Schenfisch, Anna, Schupbach, Jordan, Williams, Lucia
Publikováno v:
In Computational Geometry: Theory and Applications October 2020 90
Publikováno v:
In Journal of Quantitative Spectroscopy and Radiative Transfer 2011 112(4):577-598