In this paper, we introduce a framework for segmenting instances of a common object class by multiple active contour evolution over semantic segmentation maps of images obtained through fully convolutional networks. The contour evolution is cast as an energy minimization problem, where the aggregate energy functional incorporates a data fit term, an explicit shape model, and accounts for object overlap. Efficient solution neighborhood operators are proposed, enabling optimization through metaheuristics such as simulated annealing. We instantiate the proposed framework in the context of segmenting individual fallen stems from high-resolution aerial multispectral imagery. We validated our approach on 3 real-world scenes of varying complexity. The test plots were situated in regions of the Bavarian Forest National Park, Germany, which sustained a heavy bark beetle infestation. Evaluations were performed on both the polygon and line segment level, showing that the multi-contour segmentation can achieve up to 0.93 precision and 0.82 recall. An improvement of up to 7 percentage points (pp) in recall and 6 in precision compared to an iterative sample consensus line segment detection was achieved. Despite the simplicity of the applied shape parametrization, an explicit shape model incorporated into the energy function improved the results by up to 4 pp of recall. Finally, we show the importance of using a deep learning based semantic segmentation method as the basis for individual stem detection. Our method is a step towards increased accessibility of automatic fallen tree mapping, due to higher cost efficiency of aerial imagery acquisition compared to laser scanning. The precise fallen tree maps could be further used as a basis for plant and animal habitat modeling, studies on carbon sequestration as well as soil quality in forest ecosystems.