Euclidean and Affine Curve Reconstruction
This work addresses curve reconstruction for applications in computer vision and shape analysis, but it appears incremental as it builds on existing invariance concepts and algorithms.
The paper tackles the problem of reconstructing planar curves from prescribed Euclidean or affine curvatures, which are important for computer vision and shape analysis, by implementing algorithms and providing estimates on the closeness of reconstructed curves relative to curvature metrics.
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.