Unsigned distance fields (UDFs) offer broader modeling capabilities than signed distance fields (SDFs), enabling the representation of shapes with open boundaries, non-manifold structures or mixed curve and surface parts. However, extracting coherent meshes from UDFs is fundamentally harder, as classical grid-based iso-surfacing techniques are not applicable since they require a way to distinguish the inside from the outside of the shape. We introduce OffsetAxis, a new UDF reconstruction pipeline that supports open, non-manifold, and curve-like geometries. Our key insight is that the 0-level set extraction problem can be restated as the extraction of the medial axis of the $α$-offset volume of the UDF. This formulation unlocks mature medial-axis machinery that naturally supports boundaries, non-manifold junctions and curves. To avoid the biases of grid-based techniques, we sample the $α$-offset surface using ray casting and optimize medial balls inside the offset volume with an efficient variant of Variational Medial Axis Sampling. The final mesh is recovered by taking the dual of the connectivity of the medial ball clusters, producing structurally coherent reconstructions for a wide range of topologies. The robustness and versatility of the approach allow it to handle imperfect distance fields, including neural UDFs trained on noisy inputs, the Quasi-Medial Distance Field (Q-MDF), as well as distances computed directly on triangle soups or point clouds. Extensive experiments demonstrate that our method produces more faithful mesh reconstruction and better alignment with the underlying shape structure than prior techniques.

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