Simplification of Jacobi Sets
The Jacobi set of two Morse 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 twopiecewise linear functions may contain several components indicative of noisy or a feature-rich dataset. We pose the problem of simplification as the extraction oflevel sets and offset contours and describe an algorithm to compute and simplify Jacobi sets in a robust manner.
KeywordsInteger Linear Program Piecewise Linear Function Morse Theory Morse Function Voronoi Region
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