TopoInVis2022 Honorable Mention Award for „Reduced Connectivity for Local Bilinear Jacobi Sets“

October 17, 2022; Christina Warren

At this year's IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis2022),  Daniel Klötzl, Tim Krake, Youjia Zhou, Jonathan Stober, Kathrin Schulte, Ingrid Hotz, Bei Wang and Daniel Weiskopf received the Honorable Mention Award for their publication " Reduced Connectivity for Local Bilinear Jacobi Sets". The TopoInVis Workshop was held in conjunction with IEEE VIS 2022 in Oklahoma City, USA.

Abstract

We present a new topological connection method for the local bilinear computation of Jacobi sets that improves the visual representation while preserving the topological structure and geometric configuration. To this end, the topological structure of the local bilinear method is utilized, which is given by the nerve complex of the traditional piecewise linear method. Since the nerve complex consists of higher-dimensional simplices, the local bilinear method (visually represented by the 1-skeleton of the nerve complex) leads to clutter via crossings of line segments. Therefore, we propose a homotopy-equivalent representation that uses different collapses and edge contractions to remove such artifacts. Our new connectivity method is easy to implement, comes with only little overhead, and results in a less cluttered representation.

Fig.1: The Jacobi set is a topological descriptor that captures gradient alignments and is originally computed via a piecewise linear method. The local bilinear method introduces a more precise approximation of Jacobi sets but leads to clutter via crossings of line segments. Our reduced connectivity for local bilinear Jacobi sets is inspired by different collapsing methods and improves the visual representation while preserving the topological and geometrical structure.

  

Links:

TopoInVIS 2022