Radiance Fields have become a powerful tool for modeling 3D scenes from multiple images. However, they remain difficult to segment into semantically meaningful regions. Some methods work well using 2D semantic masks, but they generalize poorly to class-agnostic segmentations. More recent methods circumvent this issue by using contrastive learning to optimize a high-dimensional 3D feature field instead. However, recovering a segmentation then requires clustering and fine-tuning the associated hyperparameters. In contrast, we aim to identify the necessary changes in segmentation field methods to directly learn a segmentation field while being robust to inconsistent class-agnostic masks, successfully decomposing the scene into a set of objects of any class. By introducing an additional spatial regularization term and restricting the field to a limited number of competing object slots against which masks are matched, a meaningful object representation emerges that best explains the 2D supervision. Our experiments demonstrate the ability of our method to generate 3D panoptic segmentations on complex scenes, and extract high-quality 3D assets from radiance fields that can then be used in virtual 3D environments.