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Euclidean and
affine curve reconstruction
Jose Agudelo, Brooke Dippold, Ian Klein, Alex Kokot, Eric Geiger and Irina Kogan |
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Vol. 17 (2024), No. 1, 29–63
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Abstract |
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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. |
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Keywords
planar curves, Euclidean and affine transformations,
Euclidean and affine curvatures, curve reconstruction,
Picard iterations, distances
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Mathematical Subject Classification
Primary: 53A04, 53A15, 53A55
Secondary: 34A45, 68T45
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Milestones
Received: 13 February 2022
Revised: 28 January 2023
Accepted: 30 January 2023
Published: 15 March 2024
Communicated by Michael Dorff
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Authors |
| Jose Agudelo | |
| University of New Mexico Albuquerque, NM United States |
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| Brooke Dippold | |
| Longwood University Farmville, VA United States |
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| Ian Klein | |
| North Carolina State
University Raleigh, NC United States |
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| Alex Kokot | |
| University of Washington Seattle, WA United States |
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| Eric Geiger | |
| Baruch College, CUNY New York, NY United States |
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| Irina Kogan | |
| North Carolina State
University Raleigh, NC United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
