We present a filtering method for 2D curvilinear structures, called RORPO (Ranking the Orientation Responses of Path Operators). RORPO is based on path operators, a recently developed family of mathematical morphology filters. Compared with classical state of the art methods, RORPO is non–local and well adapted to the intrinsic anisotropy of curvilinear structures. Since RORPO does not depend on a linear scale-space framework, it tends to preserve object contours without a blurring effect. Due to these properties, RORPO is a useful low–level filter and can also serve as a curvilinear priori in segmentation frameworks. In this article, after introducing RORPO, we develop the 2D version of the algorithm and present a few applications.