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 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 recent foundation model SAM. 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 of the results by up to 81.6% compared to the state-of-the-art.