Efficient representation in spaces of plane curves (Q2390608)

The problem treated is connected with questions of shape recognition and analysis arising from computer vision. It is dealt with by application of ideas of sparse representation to the approximation of curves. The Blum medial axis representation of embeddings of plane curves into \(\mathbb{R}^2\) is evaluated from the perspective of efficiency using a \(C^1\)-type metric. For compact classes of curves with Lipschitz tangent angle the \(\varepsilon\)-entropy is computed. It is compared with uniform approximation using the Blum medial axis. In the compact setting the boundary curve is more efficient. For non-compact classes of embeddings a geometric criterion is established for when the medial axis will be more efficient than other approximations.