A key challenge for autonomous precision weeding is to reliably and accurately detect weed plants and crop plants in real time to minimise damage to surrounding crop plants while performing weeding actions. Specifically for a wheat farm, classifying ryegrass weed plants is particularly difficult even with human eyes since ryegrass shows visually very similar shape and texture to the crop plants themselves. A Deep Neural Network (DNN) that exploits the geometric location of ryegrass is proposed for the real time segmentation of inter-row ryegrass weeds in a wheat field. Our proposed method introduces two subnets in a conventional encoder-decoder style DNN to improve segmentation accuracy. The two subnets treat inter-row and intra-row pixels differently, and provide corrections to preliminary segmentation results of the conventional encoder-decoder DNN. A dataset captured in a wheat farm by an agricultural robot at different time instances is used to evaluate the segmentation performance, and the proposed method performs the best among various popular semantic segmentation algorithms. The proposed method runs at 48.95 Frames Per Second (FPS) with a consumer level graphics processing unit, thus is real-time deployable at camera frame rate.