Today Deep Learning (DL) is state-of-the-art in medical imaging segmentation tasks, including accurate localization of abdominal organs in MRI images. But segmentation still exhibits inaccuracies, which may be due to texture similarities, proximity or confusion between organs, morphology variations, acquisition conditions or other parameters. Examples include regions classified as the wrong organ, some noisy regions and inaccuracies near borders. To improve robustness, the DL output can be supplemented by more traditional image postprocessing operations that enforce simple semantic invariants. In this paper we define and apply totally automatic post-processing operations applying semantic invariants to correct segmentation mistakes. Organs are assigned relative spatial location restrictions (atlas fencing), 3D organ continuity requirements (envelop continuity), and smoothness constraints. A reclassification is done within organ envelopes to correct classification mistakes, and noise is removed (fencing, enveloping, noise removal, re-classifying and smoothing). Our experimental evaluation quantifies the improvement and compares the resulting quality with prior work on DL-based organ segmentation. Based on the experiments, we conclude post-processing improved the Jaccard index over independent test MRI sequences by a sum of 12 to 25 percentage points over the four segmented organs. This work has an important impact on research and practical application of DL because it describes how to post-process, quantifies the advantages, and can be applied to any DL approach.