Automated delineation of smallholder farm fields is difficult because of their small size, irregular shape and the use of mixed-cropping systems. Edges between smallholder plots are often indistinct in satellite imagery and contours have to be identified by considering the transition of the complex textural patterns of the fields. We introduce a strategy to delineate field boundaries using a fully convolutional network in combination with a globalization and grouping algorithm to produce a hierarchical segmentation of the fields. We carry out an experimental analysis in a study area in Kofa, Nigeria, using a WorldView-3 image, comparing several state-of-the-art contour detection algorithms. The proposed strategy outperforms state-of-the-art computer vision methods and shows promising results by automatically delineating field boundaries with an accuracy close to human level photo-interpretation.