  We consider the problem of estimating the curvature profile along the
boundaries of digital objects in segmented black-and-white images. We start
with the curvature estimator proposed by Roussillon et al., which is based on
the calculation of \emph{maximal digital circular arcs} (MDCA). We extend this
estimator to the $\lambda$-MDCA curvature estimator that considers several
MDCAs for each boundary pixel and is therefore smoother than the classical MDCA
curvature estimator. We prove an explicit order of convergence result for
convex subsets in $\mathbb{R}^2$ with positive, continuous curvature profile.
In addition, we evaluate the curvature estimator on various objects with known
curvature profile. We show that the observed order of convergence is close to
the theoretical limit of $\mathcal{O}(h^{\frac13})$. Furthermore, we establish
that the $\lambda$-MDCA curvature estimator outperforms the MDCA curvature
estimator, especially in the neighborhood of corners.
