212 citations · 323 across the 23 of their papers we have counts for
13 papers · 1 filter
Localized Evaluation for Constructing Discrete Vector Fields
Tanner Finken, Julien Tierny, Joshua A Levine
Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative…
Merge Tree Geodesics and Barycenters with Path Mappings
Florian Wetzels, Mathieu Pont, Julien Tierny +1
Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysi…
Parallel Computation of Piecewise Linear Morse-Smale Segmentations
Robin G. C. Maack, Jonas Lukasczyk, Julien Tierny +3
This paper presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation…
Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)
Mathieu Pont, Jules Vidal, Julien Tierny
This paper presents a computational framework for the Principal Geodesic Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis (PCA) f…
Fast Approximation of Persistence Diagrams with Guarantees
Jules Vidal, Julien Tierny
This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for…
Wasserstein Distances, Geodesics and Barycenters of Merge Trees
Mathieu Pont, Jules Vidal, Julie Delon +1
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] an…
TopoMap: A 0-dimensional Homology Preserving Projection of High-Dimensional Data
Harish Doraiswamy, Julien Tierny, Paulo J. S. Silva +2
Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data fr…
A Progressive Approach to Scalar Field Topology
Jules Vidal, Pierre Guillou, Julien Tierny
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast iden…
Statistical Parameter Selection for Clustering Persistence Diagrams
Max Kontak, Jules Vidal, Julien Tierny
In urgent decision making applications, ensemble simulations are an important way to determine different outcome scenarios based on currently available data. In this paper, we will…
Progressive Wasserstein Barycenters of Persistence Diagrams
Jules Vidal, Joseph Budin, Julien Tierny
This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensembl…
Persistence Atlas for Critical Point Variability in Ensembles
Guillaume Favelier, Noura Faraj, Brian Summa +1
This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framew…
The Topology ToolKit
Julien Tierny, Guillaume Favelier, Joshua A. Levine +2
This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, effi…
Jacobians and Hessians of Mean Value Coordinates for Closed Triangular Meshes
Jean-Marc Thiery, Julien Tierny, Tamy Boubekeur
In this technical note, we present the formulae of the derivatives of the Mean Value Coordinates based transformations, using an enclosing triangle mesh, acting as a cage for the d…