Affine geometry, curve flows, and invariant numerical approximations

Eugenio Calabi, Peter J. Olver, Allen Tannenbaum

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

A new geometric approach to the affine geometry of curves in the plane and to affine-invariant curve shortening is presented. We describe methods of approximating the affine curvature with discrete finite difference approximations, based on a general theory of approximating differential invariants of Lie group actions by joint invariants. Applications to computer vision are indicated.

Original languageEnglish (US)
Pages (from-to)154-196
Number of pages43
JournalAdvances in Mathematics
Volume124
Issue number1
DOIs
StatePublished - Dec 1 1996

Bibliographical note

Funding Information:
* Supported in part by NSF Grant DMS 92-03398. E-mail address: calabi math.upenn.edu. -Supported in part by NSF Grant DMS 95-00931. E-mail address: olver ima.umn.edu. Supported in part by NSF Grant ECS-9122106, by the Air Force Office of Scientific Research Grant F49620-94-1-00S8DEF, by Army Research Office Grants DAAL03-91-G-0019, DAAH04-93-G-0332, and DAAH04-94-G-0054, and by Image Evolutions, Ltd. E-mail address: tannenba ee.umn.edu.

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