Daniel Klötzl, Tim Krake, Youjia Zhou, Ingrid Hotz, Bei Wang and Daniel Weiskopf were awarded the Visual Computer Second Best Paper Award for their research paper "Local bilinear computation of Jacobi sets". The award was presented at the Computer Graphics International (CGI2022) conference, held online September 12-16, 2022. CGI is one of the oldest annual international computer graphics conferences in the world and was organized this year by MIRALab - CUI, University of Geneva, Switzerland and supported by the Computer Graphics Society (CGS).
We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.