Global region-based active contours, like the Chan-Vese model, often make strong assumptions on the intensity distributions of the searched object and background, preventing their use in natural images. We introduce a more flexible local region energy achieving a trade-off between local features of gradient-like terms and global region features. Relying on the theory of parallel curves, we define our region term using constant length lines normal to the contour. Mathematical derivations are performed on an explicit curve, leading to a form allowing efficient implementation on a parametric snake. However, we provide implementations on both explicit and implicit contours.