Premise: Weed removal in agriculture is typically achieved using herbicides. The use of autonomous robots to reduce weeds is a promising alternative solution, although their implementation requires the precise detection and identification of crops and weeds to allow an efficient action. Methods: We trained and evaluated an instance segmentation convolutional neural network aimed at segmenting and identifying each plant specimen visible in images produced by agricultural robots. The resulting data set comprised field images on which the outlines of 2489 specimens from two crop species and four weed species were manually drawn. We adjusted the hyperparameters of a mask region-based convolutional neural network (R-CNN) to this specific task and evaluated the resulting trained model. Results: The probability of detection using the model was quite good but varied significantly depending on the species and size of the plants. In practice, between 10% and 60% of weeds could be removed without too high of a risk of confusion with crop plants. Furthermore, we show that the segmentation of each plant enabled the determination of precise action points such as the barycenter of the plant surface. Discussion: Instance segmentation opens many possibilities for optimized weed removal actions. Weed electrification, for instance, could benefit from the targeted adjustment of the voltage, frequency, and location of the electrode to the plant. The results of this work will enable the evaluation of this type of weeding approach in the coming months.