Euclidean and affine curve reconstruction
Copyright policy )Euclidean and affine curve reconstruction
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 equi-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.
This paper is a result of an REU project conducted at the North Carolina State University in the Summer and Fall 2020. This version has several minor corrections
- University of Mary United States
- Baruch College United States
- North Carolina Agricultural and Technical State University United States
- University of New Mexico United States
- City University of New York United States
Mathematics - Differential Geometry, FOS: Computer and information sciences, Geometric methods in ordinary differential equations, Curves in Euclidean and related spaces, Hausdorff distance, 53A04, 53A15, 53A55, 34A45, 68T45, Computer Vision and Pattern Recognition (cs.CV), Affine differential geometry, Computer Science - Computer Vision and Pattern Recognition, Differential invariants (local theory), geometric objects, planar curves, Machine vision and scene understanding, affine transformations, Computer-aided design (modeling of curves and surfaces), Differential Geometry (math.DG), curve reconstruction, affine curvature, Numerical smoothing, curve fitting, FOS: Mathematics, Theoretical approximation of solutions to ordinary differential equations
Mathematics - Differential Geometry, FOS: Computer and information sciences, Geometric methods in ordinary differential equations, Curves in Euclidean and related spaces, Hausdorff distance, 53A04, 53A15, 53A55, 34A45, 68T45, Computer Vision and Pattern Recognition (cs.CV), Affine differential geometry, Computer Science - Computer Vision and Pattern Recognition, Differential invariants (local theory), geometric objects, planar curves, Machine vision and scene understanding, affine transformations, Computer-aided design (modeling of curves and surfaces), Differential Geometry (math.DG), curve reconstruction, affine curvature, Numerical smoothing, curve fitting, FOS: Mathematics, Theoretical approximation of solutions to ordinary differential equations
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