Anomaly segmentation is an essential capability for safety-critical robotics applications that must be aware of unexpected events. Normalizing flows (NFs), a class of generative models, are a promising approach for this task due to their ability to model the inlier data distribution efficiently. However, their performance falters in dynamic scenes, where complex, multi-modal data distributions cause them to struggle with identifying out-of-distribution samples, leaving a performance gap to leading discriminative methods. To address this limitation, we introduce FlowCLAS, a hybrid framework that enhances the traditional maximum likelihood objective of NFs with a discriminative, contrastive loss. Leveraging Outlier Exposure, this objective explicitly enforces a separation between normal and anomalous features in the latent space, retaining the probabilistic foundation of NFs while embedding the discriminative power they lack. The strength of this approach is demonstrated by FlowCLAS establishing new state-of-the-art (SOTA) performance across multiple challenging anomaly segmentation benchmarks for robotics, including Fishyscapes Lost & Found, Road Anomaly, SegmentMeIfYouCan-ObstacleTrack, and ALLO. Our experiments also show that this contrastive approach is more effective than other outlier-based training strategies for NFs, successfully bridging the performance gap to leading discriminative methods. Project page: https://trailab.github.io/FlowCLAS

We study the problem of approximating a 3D solid with a union of overlapping spheres. In comparison with a state-of-the-art approach, our method offers more than an order of magnitude speedup and achieves a tighter approximation in terms of volume difference with the original solid while using fewer spheres. The spheres generated by our method are internal and tangent to the solid's boundary, which permits an exact error analysis, fast updates under local feature size preserving deformation, and conservative dilation. We show that our dilated spheres offer superior time and error performance in approximate separation distance tests than the state-of-the-art method for sphere set approximation for the class of (σ,θ)-fat solids. We envision that our sphere-based approximation will also prove useful for a range of other applications, including shape matching and shape segmentation.