Simplification of Jacobi sets.

Suthambhara N. and Vijay Natarajan.
In Topological Data Analysis and Visualization: Theory, Algorithms and Applications., Valerio Pascucci, Xavier Tricoche, Hans Hagen, and Julien Tierny (editors), Springer-Verlag, Mathematics and Visualization Series, 2011, 91-102.

Abstract

The Jacobi set of twoMorse functions defined on a 2-manifold is the collection of points where the gradients of the functions align with each other or where one of the gradients vanish. It describes the relationship between functions defined on the same domain, and hence plays an important role in multi-field visualization. The Jacobi set of two piecewise linear functions may contain several components indicative of noisy or a feature-rich dataset. We pose the problem of simplification as the extraction of level sets and offset contours and describe.

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