  The Jacobi set of a bivariate scalar field is the set of points where the
gradients of the two constituent scalar fields align with each other. It
captures the regions of topological changes in the bivariate field. The Jacobi
set is a bivariate analog of critical points, and may correspond to features of
interest. In the specific case of time-varying fields and when one of the
scalar fields is time, the Jacobi set corresponds to temporal tracks of
critical points, and serves as a feature-tracking graph. The Jacobi set of a
bivariate field or a time-varying scalar field is complex, resulting in
cluttered visualizations that are difficult to analyze. This paper addresses
the problem of Jacobi set simplification. Specifically, we use the time-varying
scalar field scenario to introduce a method that computes a reduced Jacobi set.
The method is based on a stability measure called robustness that was
originally developed for vector fields and helps capture the structural
stability of critical points. We also present a mathematical analysis for the
method, and describe an implementation for 2D time-varying scalar fields.
Applications to both synthetic and real-world datasets demonstrate the
effectiveness of the method for tracking features.
