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Euclidean and affine curve reconstruction

Jose Agudelo, Brooke Dippold, Ian Klein, Alex Kokot, Eric Geiger and Irina Kogan

Vol. 17 (2024), No. 1, 29–63

We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the special affine groups, respectively, and play an important role in computer vision and shape analysis. We discuss and implement algorithms for such reconstruction, and give estimates on how close reconstructed curves are relative to the closeness of their curvatures in appropriate metrics. Several illustrative examples are provided.

planar curves, Euclidean and affine transformations, Euclidean and affine curvatures, curve reconstruction, Picard iterations, distances
Mathematical Subject Classification
Primary: 53A04, 53A15, 53A55
Secondary: 34A45, 68T45
Received: 13 February 2022
Revised: 28 January 2023
Accepted: 30 January 2023
Published: 15 March 2024

Communicated by Michael Dorff
Jose Agudelo
University of New Mexico
Albuquerque, NM
United States
Brooke Dippold
Longwood University
Farmville, VA
United States
Ian Klein
North Carolina State University
Raleigh, NC
United States
Alex Kokot
University of Washington
Seattle, WA
United States
Eric Geiger
Baruch College, CUNY
New York, NY
United States
Irina Kogan
North Carolina State University
Raleigh, NC
United States