  Semantic segmentation models are typically trained on a fixed set of classes,
limiting their applicability in open-world scenarios. Class-incremental
semantic segmentation aims to update models with emerging new classes while
preventing catastrophic forgetting of previously learned ones. However,
existing methods impose strict rigidity on old classes, reducing their
effectiveness in learning new incremental classes. In this work, we propose
Taxonomy-Oriented Poincar\'e-regularized Incremental-Class Segmentation
(TOPICS) that learns feature embeddings in hyperbolic space following explicit
taxonomy-tree structures. This supervision provides plasticity for old classes,
updating ancestors based on new classes while integrating new classes at
fitting positions. Additionally, we maintain implicit class relational
constraints on the geometric basis of the Poincar\'e ball. This ensures that
the latent space can continuously adapt to new constraints while maintaining a
robust structure to combat catastrophic forgetting. We also establish eight
realistic incremental learning protocols for autonomous driving scenarios,
where novel classes can originate from known classes or the background.
Extensive evaluations of TOPICS on the Cityscapes and Mapillary Vistas 2.0
benchmarks demonstrate that it achieves state-of-the-art performance. We make
the code and trained models publicly available at
http://topics.cs.uni-freiburg.de.
