Minimum description length arc spline approximation of digital curves

We present a method for an unsupervised two model approximation of digital curves. For any maximum tolerance, we obtain the minimum number of smoothly joined circular arcs and line segments. The breakpoints of the resulting curve are neither restricted to be pixel discrete nor they have to be chosen from a finite set of points. Instead, they are computed automatically. This has a considerably positive effect on the number of segments. In addition, we present a very efficient way to encode the approximating curve. Thus, we achieve the minimum description length for any tolerance. The performance of the proposed method is illustrated by different examples including characteristics as the description length, the fitting error and the length-angle representation.