Abstract: We address the automatic pixelwise labeling of satellite images with convolutional neural networks. These networks tend to lose spatial precision in the process, outputting coarse classification maps that do not accurately outline the objects. While specific enhancement algorithms have been designed in the literature to improve such coarse neural network outputs, this requires a decision-making process to choose and tune the right enhancement algorithm. Instead, we aim at learning the enhancement algorithm itself. We consider the class of partial differential equations, see them as iterative enhancement processes, and observe that they can be expressed as recurrent neural networks. Consequently, we train a recurrent neural network from manually labeled data for our enhancement task. In a series of experiments we show that our network effectively learns an iterative process that significantly improves the quality of satellite image classification maps.