Euclidean and Affine Curve Reconstruction

TL;DR

This paper explores algorithms for reconstructing planar curves from their Euclidean or affine curvatures, emphasizing invariance properties and providing estimates on reconstruction accuracy with practical examples.

Contribution

It introduces practical algorithms for curve reconstruction based on Euclidean and affine curvatures, including error estimates and illustrative examples.

Findings

Algorithms successfully reconstruct curves from curvature data.

Reconstruction accuracy correlates with curvature closeness in specific metrics.

Practical implementation demonstrates effectiveness in shape analysis.

Abstract

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.