Deep learning models for semantic segmentation of images require large amounts of data. In the medical imaging domain, acquiring sufficient data is a significant challenge. Labeling medical image data requires expert knowledge. Collaboration between institutions could address this challenge, but sharing medical data to a centralized location faces various legal, privacy, technical, and data-ownership challenges, especially among international institutions. In this study, we introduce the first use of federated learning for multi-institutional collaboration, enabling deep learning modeling without sharing patient data. Our quantitative results demonstrate that the performance of federated semantic segmentation models (Dice=0.852) on multimodal brain scans is similar to that of models trained by sharing data (Dice=0.862). We compare federated learning with two alternative collaborative learning methods and find that they fail to match the performance of federated learning.