--- _id: '3989' abstract: - lang: eng text: We introduce local and global comparison measures for a collection of k less than or equal to 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 ace easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets. author: - first_name: Herbert full_name: Herbert Edelsbrunner id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: John full_name: Harer, John last_name: Harer - first_name: Vijay full_name: Natarajan, Vijay last_name: Natarajan - first_name: Valerio full_name: Pascucci, Valerio last_name: Pascucci citation: ama: 'Edelsbrunner H, Harer J, Natarajan V, Pascucci V. Local and global comparison of continuous functions. In: IEEE; 2004:275-280. doi:10.1109/VISUAL.2004.68' apa: 'Edelsbrunner, H., Harer, J., Natarajan, V., & Pascucci, V. (2004). Local and global comparison of continuous functions (pp. 275–280). Presented at the VIS: IEEE Visualization, IEEE. https://doi.org/10.1109/VISUAL.2004.68' chicago: Edelsbrunner, Herbert, John Harer, Vijay Natarajan, and Valerio Pascucci. “Local and Global Comparison of Continuous Functions,” 275–80. IEEE, 2004. https://doi.org/10.1109/VISUAL.2004.68. ieee: 'H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, “Local and global comparison of continuous functions,” presented at the VIS: IEEE Visualization, 2004, pp. 275–280.' ista: 'Edelsbrunner H, Harer J, Natarajan V, Pascucci V. 2004. Local and global comparison of continuous functions. VIS: IEEE Visualization, 275–280.' mla: Edelsbrunner, Herbert, et al. Local and Global Comparison of Continuous Functions. IEEE, 2004, pp. 275–80, doi:10.1109/VISUAL.2004.68. short: H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, in:, IEEE, 2004, pp. 275–280. conference: name: 'VIS: IEEE Visualization' date_created: 2018-12-11T12:06:18Z date_published: 2004-10-01T00:00:00Z date_updated: 2021-01-12T07:53:41Z day: '01' doi: 10.1109/VISUAL.2004.68 extern: 1 month: '10' page: 275 - 280 publication_status: published publisher: IEEE publist_id: '2137' quality_controlled: 0 status: public title: Local and global comparison of continuous functions type: conference year: '2004' ...