This paper focuses on the estimation of local orientation in an image where several orientations exist at the same location and at the same scale. Within this framework, IRON, an operator based on an oriented network of parallel lines is introduced. IRON uses only a few parameters. Beyond the choice of a specific line homogeneity feature, the size and the shape of the network can be tuned. These parameters allow us to adapt our operator to the image studied. The implementation we propose for the network is recursive, relying on the rotation of the image instead of the rotation of the operator. IRON can proceed on a small computing support, and thus provides a local estimation of orientations. Herein, we test IRON on both synthetic and real images. Compared to some other orientation estimation methods such as Gabor filters or Steerable filters, our operator detects multiple orientations with both better accuracy and noise robustness, at a competitive computational cost thanks to its recursivity. Moreover, IRON offers better selectivity, particularly at small scale.