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Analyzing scenes thoroughly is crucial for mobile robots acting in different environments. Semantic segmentation can enhance various subsequent tasks, such as (semantically assisted) person perception, (semantic) free space detection, (semantic) mapping, and (semantic) navigation. In this paper, we propose an efficient and robust RGB-D segmentation approach that can be optimized to a high degree using NVIDIA TensorRT and, thus, is well suited as a common initial processing step in a complex system for scene analysis on mobile robots. We show that RGB-D segmentation is superior to processing RGB images solely and that it can still be performed in real time if the network architecture is carefully designed. We evaluate our proposed Efficient Scene Analysis Network (ESANet) on the common indoor datasets NYUv2 and SUNRGB-D and show that we reach state-of-the-art performance while enabling faster inference. Furthermore, our evaluation on the outdoor dataset Cityscapes shows that our approach is suitable for other areas of application as well. Finally, instead of presenting benchmark results only, we also show qualitative results in one of our indoor application scenarios.