While sugar beets are stored prior to processing, they lose sugar due to factors such as microorganisms present in adherent soil and excess vegetation. Their automated visual inspection promises to aide in quality assurance and thereby increase efficiency throughout the processing chain of sugar production. In this work, we present a novel high-quality annotated dataset and two-stage method for the detection, semantic segmentation and mass estimation of post-harvest and post-storage sugar beets in monocular RGB images. We conduct extensive ablation experiments for the detection of sugar beets and their fine-grained semantic segmentation regarding damages, rot, soil adhesion and excess vegetation. For these tasks, we evaluate multiple image sizes, model architectures and encoders, as well as the influence of environmental conditions. Our experiments show an mAP50-95 of 98.8 for sugar-beet detection and an mIoU of 64.0 for the best-performing segmentation model.