Estimation of the curvature of an interface from a digital 2D image

In this paper a method for the estimation of the curvature along a condensed phase interface is presented. In a previous paper in this journal [J.W. Bullard, E.J. Garboczi, W.C. Carter, E.R. Fuller Jr., Computational Materials Science 4 (1995) 103–116] a mathematical relationship was established between this curvature and a template disk located at a given point along the interface. The portion of the computed area of the template disk covering one of the phases was shown to be asymptotically linear in the curvature. Instead of utilizing this relationship, an empirical approach was proposed in Bullard et al. in order to compensate for discrete uncertainties. In this paper, we show that this linear relationship can be used directly along the interface avoiding the empirical approach proposed earlier. Modifications of the algorithm are however needed, and with good data smoothing techniques, our method provides good quantitative curvature estimates.