Showing papers by "Herbert Edelsbrunner published in 2015"
TL;DR: The persistence of the eigenspaces is defined, effectively introducing a hierarchical organization of the map in a continuous self-map and the induced endomorphism on homology.
Abstract: Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.
48 citations
TL;DR: A software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes that constructs a geometric graph representation together with the function that records the time of growth.
Abstract: We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth.
43 citations
TL;DR: The dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation, providing the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.
Abstract: We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.
18 citations
Posted Content•
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TL;DR: In this paper, the authors study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover, and measure the quality by the probability that a random point lies in exactly one disk.
Abstract: Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations.
5 citations
5 citations
Proceedings Article•
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TL;DR: In this article, the authors study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover, and measure the quality by the probability that a random point lies in exactly one disk.
Abstract: Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations.
2 citations
1 citations
TL;DR: The authors' computeraided classification system could provide effective recognition of three main types of gastric mucosal patterns and thus may lead to pathology predict ion and supporting of clinical decision.
TL;DR: The Yaroslavl International Conference on Discrete Geometry dedicated to the centenary of A.D. Alexandrov was organized by the International B.N. Delaunay Laboratory "Discrete and Computational Geometry" and took place from August 13 to 18, 2012 at the P.G. Demidov YaroslavL State University.
Abstract: The Yaroslavl International Conference on Discrete Geometry dedicated to the centenary of A.D. Alexandrov was organized by the International B.N. Delaunay Laboratory \"Discrete and Computational Geometry\" and took place from August 13 to 18, 2012 at the P.G. Demidov Yaroslavl State University. The purpose of this note is to highlight the main results presented at the conference and to discuss the role of the meeting in the development of the field of Discrete and Computational Geometry in Yaroslavl. The article is published in the author’s wording.