A Probabilistic Perspective on Wasserstein-Based Evidential Uncertainty for Out-of-Distribution Segmentation

Semantic segmentation networks operate on a fixed set of classes and therefore fail when out-of-distribution (OOD) objects appear during deployment, a critical limitation for safety-critical applications such as autonomous driving. Reliably identifying OOD objects requires well-calibrated epistemic uncertainty, yet common softmax-based confidence scores remain overconfident, while Bayesian alternatives such as Monte Carlo dropout or deep ensembles require costly repeated forward passes. Evidential Deep Learning (EDL) offers an efficient alternative by modeling class probabilities as a Dirichlet distribution learned from a single deterministic forward pass. Existing EDL formulations rely on Euclidean objectives that push predictions towards the simplex vertices, encouraging overconfidence rather than preserving uncertainty for unfamiliar inputs. We instead employ Wasserstein-based objectives, which respect the geometry of the probability simplex, and study the influence of the Wasserstein order on segmentation accuracy and OOD detection within a unified evidential framework. We evaluate this framework on a convolutional (DeepLabV3+) and a transformer-based (SegFormer) architecture on the SegmentMeIfYouCan benchmark, including LostAndFound, RoadObstacle21, RoadAnomaly21, and Fishyscapes. Our results show the optimal Wasserstein order is architecture-dependent: second-order objectives dominate on the convolutional backbone, third-order objectives on the transformer backbone, and our framework surpasses comparable baselines on most metrics, with a single deterministic forward pass.