We propose a novel energy term to make the curve evolution quite robust to spurious edges. The physical intuition behind the formulation is that an object edge is generally continuous, but it could be composed of weak and strong segments. We then formulate the energy term which depends on a second order measure defined on the contour. Minimisation of this energy term yields a space varying curvature based curve evolution equation. An added advantage of the formulation is that this term also acts as the regularising term for smoothing the curve evolution. The proposed term can therefore be used in conjunction with any of the numerous gradient based active contour models. For our experimentation purpose, we have used the well-known gradient vector force model as the external force. We have performed a number of experiments on images and obtained good results.