Dense pixel-wise classification maps output by deep neural networks are of extreme importance for scene understanding. However, these maps are often partially inaccurate due to a variety of possible factors. Therefore, we propose to interactively refine them within a framework named DISCA (Deep Image Segmentation with Continual Adaptation). It consists of continually adapting a neural network to a target image using an interactive learning process with sparse user annotations as ground-truth. We show through experiments on three datasets using synthesized annotations the benefits of the approach, reaching an IoU improvement up to 4.7% for ten sampled clicks. Finally, we exhibit that our approach can be particularly rewarding when it is faced to additional issues such as domain adaptation.