We introduce a robust image segmentation method based on a variational formulation using edge flow vectors. We demonstrate the non-conservative nature of this flow field, a feature that helps in a better segmentation of objects with concavities. A multi-scale version of this method is developed and is shown to improve the localization of the object boundaries. We compare and contrast the proposed method with well known state-of-the-art methods. Detailed experimental results are provided on both synthetic and natural images that demonstrate that the proposed approach is quite competitive.