Automated segmentation of individual calf muscle compartments from 3D magnetic resonance (MR) images is essential for developing quantitative biomarkers for muscular disease progression and its prediction. Achieving clinically acceptable results is a challenging task due to large variations in muscle shape and MR appearance. Although deep convolutional neural networks (DCNNs) achieved improved accuracy in various image segmentation tasks, certain problems such as utilizing long-range information and incorporating high-level constraints remain unsolved. We present a novel fully convolutional network (FCN), called FilterNet, that utilizes contextual information in a large neighborhood and embeds edge-aware constraints for individual calf muscle compartment segmentations. An encoder-decoder architecture with flexible backbone blocks is used to systematically enlarge convolution receptive field and preserve information at all resolutions. Edge positions derived from the FCN output muscle probability maps are explicitly regularized using kernel-based edge detection in an end-to-end optimization framework. Our FilterNet was evaluated on 40 T1-weighted MR images of 10 healthy and 30 diseased subjects by 4-fold cross-validation. Mean DICE coefficients of 88.00%--91.29% and mean absolute surface positioning errors of 1.04--1.66 mm were achieved for the five 3D muscle compartments.