Many applications in image processing and computer vision rely on geometric properties of curves, in particular their curvatures. Another important, but less exploited, property is the torsion for curves in space. Several methods of estimating the curvature of plane curves are known, most of them for digital curves. In this dissertation we survey these methods and propose a new method based on approximations by parabolic and cubic curves. We present a theoretical analysis of this method and also study the effect of noise. The new estimator is compared to other estimators and is seen to be very robust.