Automatically generating pedestrian pathways from aerial images requires producing a connected network suitable for routing, not just detecting where sidewalks appear. Sidewalks and crossings, in contrast to roads, may be partially occluded, implicitly defined, and exhibit complex connectivity patterns. Existing segmentation-based approaches focus on labeling pixels to infer segments, but often produce disconnected or fragmentary graphs that are unreliable for navigation. We introduce TraversRL, a vision-conditioned model that iteratively grows a pathway network from an aerial image, simulating a traveler navigating the built environment. TraversRL uses an action space of short and long direction-distance segments designed to adapt to complex patterns and span occlusions, and uses a combination of graph-level and step-wise rewards to balance overall connectivity with precise edge placement. Across three visual backbones and three intersection datasets, TraversRL substantially improves buffered IoU with the ground-truth graph relative to a state-of-the-art segmentation baseline, and more than doubles metrics of connectivity. Moreover, combining global and local rewards produces cleaner graphs with fewer spurious branches while further improving overall performance. These results demonstrate that modeling pathway extraction as a sequential decision process from the perspective of a traveler, while optimizing for final graph quality with reinforcement learning, produces significantly more reliable pedestrian networks.
Vision transformers have become a dominant architecture for visual recognition. However, standard models do not explicitly encode the planar symmetries that arise in many vision domains. We introduce a family of vision transformers equivariant to arbitrary discrete subgroups of $\mathrm{O}(2)$, providing a unified framework that generalizes prior flipping- and $D_4$-equivariant transformer architectures. Our construction yields equivariant analogues of the core transformer components, together with expressivity guarantees for the resulting layers. In particular, we show that whenever $H \le G$, the class of $G$-equivariant ViTs embeds naturally into the class of $H$-equivariant ViTs. We also prove that, in the single-head setting, the corresponding equivariant self-attention layer realizes every $G$-equivariant self-attention map representable by ordinary self-attention. We further construct a $D_6$-equivariant model based on hexagonal patches, making the architecture compatible with six-fold rotational symmetries. We evaluate the resulting models on the PatternNet aerial image dataset in artificially data-scarce regimes across subgroups of $D_4$ and $D_6$. Our experiments compare two equivariant attention mechanisms and analyze how the choice of homogeneous-space configurations used in the nonlinearities affects performance. Preliminary results under matched parameter budgets indicate that equivariance can improve recognition accuracy, motivating further study of how discrete symmetry groups shape transformer-based visual recognition models.