We propose an approach for Open-World Instance Segmentation (OWIS), a task that aims to segment arbitrary unknown objects in images by generalizing from a limited set of annotated object classes during training. Our Segment Object System (SOS) explicitly addresses the generalization ability and the low precision of state-of-the-art systems, which often generate background detections. To this end, we generate high-quality pseudo annotations based on the foundation model SAM [27]. We thoroughly study various object priors to generate prompts for SAM, explicitly focusing the foundation model on objects. The strongest object priors were obtained by self-attention maps from self-supervised Vision Transformers, which we utilize for prompting SAM. Finally, the post-processed segments from SAM are used as pseudo annotations to train a standard instance segmentation system. Our approach shows strong generalization capabilities on COCO, LVIS, and ADE20k datasets and improves on the precision by up to 81.6% compared to the state-of-the-art. Source code is available at:  https://github.com/chwilms/SOS .