Computing Curvature, Mean Curvature and Weighted Mean Curvature

Traditional computing methods for curvatures require the image to be second-order differentiable. Such requirement is not always satisfied, especially at sharp edges. In this paper, we propose a novel method that can compute curvatures without requiring the image second-order differentiable. We first establish the link between various curvatures and the standard Laplace operator. Then we propose to compute curvatures by a half kernel Laplace method. Our method has a smaller support region and thus is more accurate than traditional methods. It can be further adopted to compute curvature, mean curvature, and weighted mean curvature. Our method is compared with the classical schemes on both synthetic and real images, showing its effectiveness and efficiency.