Crop segmentation is an important task in Precision Agriculture, where the use of aerial robots with an on-board camera has contributed to the development of new solution alternatives. We address the problem of fig plant segmentation in top-view RGB (Red-Green-Blue) images of a crop grown under open-field difficult circumstances of complex lighting conditions and non-ideal crop maintenance practices defined by local farmers. We present a Convolutional Neural Network (CNN) with an encoder-decoder architecture that classifies each pixel as crop or non-crop using only raw colour images as input. Our approach achieves a mean accuracy of 93.85% despite the complexity of the background and a highly variable visual appearance of the leaves. We make available our CNN code to the research community, as well as the aerial image data set and a hand-made ground truth segmentation with pixel precision to facilitate the comparison among different algorithms.