Institute for Data Analysis and Visualization

We introduce local and global comparison measures for a collection of $k \leq d$ real-valued smooth functions on a common $d$-dimensional Riemannian manifold. For $k = d = 2$ we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they are easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets.