This work has been accepted by IEEE TGRS for publication in a future issue. Choosing how to encode a realworld problem as a machine learning task is an important design decision in machine learning. The task of glacier calving front modeling has often been approached as a semantic segmentation task. Recent studies have shown that combining segmentation with edge detection can improve the accuracy of calving front detectors. Building on this observation, we completely rephrase the task as a contour tracing problem and propose a model for explicit contour detection that does not incorporate any dense predictions as intermediate steps. The proposed approach, called "Charting Outlines by Recurrent Adaptation" (COBRA), combines Convolutional Neural Networks (CNNs) for feature extraction and active contour models for the delineation. By training and evaluating on several large-scale datasets of Greenland's outlet glaciers, we show that this approach indeed outperforms the aforementioned methods based on segmentation and edgedetection. Finally, we demonstrate that explicit contour detection has benefits over pixel-wise methods when quantifying the models' prediction uncertainties. The project page containing the code and animated model predictions can be found at https://khdlr.github.io/COBRA/.