# Reduced Connectivity for Local Bilinear Jacobi Sets

arXiv: https://arxiv.org/abs/2208.07148 · HTML: https://mlsanity.com/paper/2208.07148/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2022.

## Built on by (most cited first, 2 of 2)

- [Jacobi Set Simplification for Tracking Topological Features in Time-Varying Scalar Fields](https://mlsanity.com/paper/2407.03348/) (2024)
- [Extracting Complex Topology from Multivariate Functional Approximation: Contours, Jacobi Sets, and Ridge-Valley Graphs](https://mlsanity.com/paper/2508.07637/) (2025)

## Abstract (arXiv)

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.