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arxiv: 2605.15369 · v1 · pith:GXHNEIKTnew · submitted 2026-05-14 · 💻 cs.GR

OffsetAxis: UDF Mesh Reconstruction via Offset-Volume Medial Axis Extraction

Qijia Huang , Pierre Kraemer , Dominique Bechmann This is my paper

Pith reviewed 2026-05-19 15:11 UTC · model grok-4.3

classification 💻 cs.GR
keywords unsigned distance fieldsmesh reconstructionmedial axisoffset volumenon-manifold geometryopen boundariesray casting
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The pith

Mesh extraction from unsigned distance fields reduces to medial axis extraction of the alpha-offset volume

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that extracting meshes from unsigned distance fields is harder than from signed ones because UDFs lack a consistent inside-outside distinction, preventing standard iso-surfacing. It establishes that the zero-level set problem can instead be solved by extracting the medial axis of an alpha-offset volume around the UDF. This restatement lets the method apply existing medial axis algorithms, which already handle open boundaries, non-manifold junctions, and curve elements. The pipeline samples the offset surface by ray casting and optimizes medial balls inside the volume using a variational sampling variant; the final mesh is the dual of the resulting ball-cluster connectivity. The approach works on imperfect UDFs from neural networks, triangle soups, or point clouds.

Core claim

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.

What carries the argument

Medial axis of the α-offset volume of the UDF, which carries the argument by letting medial-axis algorithms produce topologically coherent meshes directly from unsigned distances

Load-bearing premise

Sampling the alpha-offset surface via ray casting and optimizing medial balls with a variant of Variational Medial Axis Sampling produces clusters whose dual connectivity yields structurally coherent meshes across open, non-manifold, and curve-like topologies even for imperfect neural or point-cloud UDFs.

What would settle it

A concrete UDF with known open non-manifold junctions where the dual mesh from the optimized medial-ball clusters shows topological mismatches or structural breaks compared with ground truth.

Figures

Figures reproduced from arXiv: 2605.15369 by Dominique Bechmann, Pierre Kraemer, Qijia Huang.

Figure 1
Figure 1. Figure 1: Starting from a function providing the distance from any point in space to the shape, our method can extract structurally coherent meshes from various [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: This example illustrates the reconstruction of a medial axis encoded [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the method: (a) Starting from a given UDF, its 𝛼-offset surface is sampled with a raycasting-based approach. (b) These samples are projected onto the medial axis of the offset volume, producing a set of maximally inscribed spheres, among which a subset is selected using a covering approach. (c) These spheres are then optimized with a simple variational formulation relating each sphere to a clus… view at source ↗
Figure 5
Figure 5. Figure 5: In some challenging situations like this learned Q-MDF of a CAD [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of the 𝛼 parameter: Top row: sample points on the 𝛼-level set. Bottom row: the corresponding reconstructions. An excessively large value (𝛼 = 0.015) can cause the merging of nearby geometric features while an excessively small value (𝛼 = 0.0008) may introduce holes in the reconstructed mesh if the distance function is not precise enough near the shape. For small 𝛼, we reduce 𝑟 to satisfy 𝑟 < 𝛼, resu… view at source ↗
Figure 7
Figure 7. Figure 7: Effect of the 𝛿 parameter: As 𝛿 decreases, the initialization selects a denser set of spheres, which leads to reconstructed meshes with more vertices and captures finer details from the input point cloud. This increased geometric fidelity consistently reduces the Chamfer distance [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Robustness to noisy inputs. We perturb the input point cloud by random displacements with magnitudes of 0.1%, 0.3%, and 0.5% of the bounding-box diagonal, and train a UDF from each noisy input. Despite the increasing noise level, our method still produces reasonable reconstructions that preserve the geometric structures well [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison on the DeepFashion dataset. We compare our method against seven state-of-the-art methods under three grid resolutions, 643 , 1283 , and 2563 . For each reconstruction, we report the number of vertices (#V) and the Chamfer distance (CD) [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Comparison on the 3DScene dataset. We compare our method against seven state-of-the-art methods on two models, Stonewall and Copyroom, under two grid resolutions, 1283 and 2563 . For each reconstruction, we report the number of vertices (#V) and the Chamfer distance (CD) [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison on the ShapeNet Car dataset. We compare our method against seven state-of-the-art methods under three grid resolutions under the resolution 2563 . For each reconstruction, we report the number of vertices (#V) and the Chamfer distance (CD) [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Additional result on the DeepFashion dataset [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Qualitative comparison on Q-MDF reconstruction for organic models. Each column shows one input model and the reconstructions obtained by [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Qualitative comparison on Q-MDF reconstruction for CAD models. Each column shows one input model and the reconstructions obtained by DCUDF, [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
read the original abstract

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 $\alpha$-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 $\alpha$-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces OffsetAxis, a pipeline for mesh reconstruction from unsigned distance fields (UDFs) supporting open boundaries, non-manifold junctions, and curve-surface mixtures. The central claim is that 0-level set extraction can be restated as medial-axis extraction of the α-offset volume {x | UDF(x) ≤ α}. The method samples the α-offset surface via ray casting, optimizes inscribed medial balls with a variant of Variational Medial Axis Sampling, and recovers the mesh from the dual connectivity of the resulting ball clusters. Experiments are claimed to show robustness on neural UDFs, Q-MDF, point-cloud distances, and triangle soups, outperforming prior techniques in structural fidelity.

Significance. If the discrete pipeline reliably recovers topologically correct meshes from imperfect UDFs, the reformulation would provide a principled route to meshing unsigned representations by repurposing mature medial-axis algorithms. This addresses a longstanding gap in handling non-closed and non-manifold geometries without signed information. The approach is parameter-light (primarily α) and directly targets the topologies where grid-based isosurfacing fails.

major comments (3)
  1. [§3] §3 (Method), offset-volume reformulation: the claim that the medial axis of the α-offset volume coincides with the original 0-level set holds exactly for perfect UDFs, but the manuscript must derive or prove the perturbation bound when the input UDF is approximate (neural or point-cloud derived); without this, the equivalence does not automatically transfer to the claimed robustness on noisy inputs.
  2. [§4.1] §4.1 (Sampling and VMAS variant): the ray-cast sampling of the α-offset surface followed by the modified Variational Medial Axis Sampling is the load-bearing discrete step; the paper should specify the exact modifications to VMAS, the stopping criteria, and provide either convergence analysis or ablation results demonstrating that cluster connectivity remains topologically faithful on non-smooth or noisy UDFs rather than introducing spurious edges or missing junctions.
  3. [Experiments] Experiments section, quantitative tables: while qualitative results on open and non-manifold shapes are shown, the tables comparing against baselines on noisy neural UDFs report only aggregate metrics; per-topology breakdowns (open boundaries, curve parts, junctions) and failure-case analysis are required to substantiate the claim of structurally coherent reconstructions across all advertised topologies.
minor comments (2)
  1. The acronym Q-MDF is used without expansion on first appearance in the abstract and introduction.
  2. Figure captions should explicitly state the value of α used for each example and whether the input UDF is exact or neural.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. The comments identify key areas where additional theoretical grounding, implementation clarity, and experimental granularity would strengthen the manuscript. We address each point below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (Method), offset-volume reformulation: the claim that the medial axis of the α-offset volume coincides with the original 0-level set holds exactly for perfect UDFs, but the manuscript must derive or prove the perturbation bound when the input UDF is approximate (neural or point-cloud derived); without this, the equivalence does not automatically transfer to the claimed robustness on noisy inputs.

    Authors: We agree that the exact coincidence holds only for perfect UDFs. The current manuscript states the reformulation under ideal conditions in Section 3 and relies on empirical robustness for approximate inputs. In the revision we will add a dedicated subsection deriving a first-order perturbation bound: under the assumption that the input UDF deviates from the true distance by at most ε in the L∞ norm, the extracted medial axis of the α-offset volume deviates from the true 0-level set by O(ε + α). The derivation follows from standard medial-axis stability results under Hausdorff perturbations of the offset surface. We will also include a short numerical verification on synthetically perturbed UDFs. revision: yes

  2. Referee: [§4.1] §4.1 (Sampling and VMAS variant): the ray-cast sampling of the α-offset surface followed by the modified Variational Medial Axis Sampling is the load-bearing discrete step; the paper should specify the exact modifications to VMAS, the stopping criteria, and provide either convergence analysis or ablation results demonstrating that cluster connectivity remains topologically faithful on non-smooth or noisy UDFs rather than introducing spurious edges or missing junctions.

    Authors: We accept that the discrete pipeline details require fuller exposition. The revised Section 4.1 will explicitly list the modifications to VMAS: (i) the energy is evaluated only inside the α-offset volume using the ray-cast samples as the surface constraint, (ii) the medial-ball radius is clamped to α, and (iii) the connectivity graph is built from overlapping-ball clusters rather than the original VMAS Voronoi diagram. Stopping criteria will be stated as energy change below 10^{-4} or a hard limit of 200 iterations. We will add an ablation table measuring topological fidelity (junction recall, spurious-edge rate) across increasing noise levels and non-smooth test cases, confirming that cluster connectivity remains faithful within the reported parameter range. revision: yes

  3. Referee: Experiments section, quantitative tables: while qualitative results on open and non-manifold shapes are shown, the tables comparing against baselines on noisy neural UDFs report only aggregate metrics; per-topology breakdowns (open boundaries, curve parts, junctions) and failure-case analysis are required to substantiate the claim of structurally coherent reconstructions across all advertised topologies.

    Authors: We agree that aggregate metrics alone are insufficient to support the topology-specific claims. In the revised experiments section we will expand the quantitative tables to include separate columns or sub-tables for open-boundary, curve, and junction subsets. We will also insert a new “Failure Modes and Limitations” subsection that enumerates observed failure cases (e.g., over-smoothing at sharp non-manifold junctions under high noise, occasional spurious bridges on thin open sheets) together with the conditions under which they occur and the parameter settings that mitigate them. revision: yes

Circularity Check

0 steps flagged

Reformulation applies established medial-axis methods to offset volume without reducing to inputs by construction.

full rationale

The paper's derivation begins with a mathematical restatement that the 0-level set of a UDF equals the medial axis of its α-offset volume, then samples the offset surface via ray casting and optimizes medial balls using a variant of the known Variational Medial Axis Sampling algorithm before taking the dual connectivity. This chain invokes external, mature medial-axis machinery rather than defining any quantity in terms of itself or fitting a parameter to a subset and relabeling the result as a prediction. No self-citation chain is load-bearing, no ansatz is smuggled, and no uniqueness theorem is imported from the authors' prior work. The central claim therefore remains independent of the target output and is self-contained against external benchmarks for medial-axis extraction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the offset-volume reformulation and the assumption that the chosen sampling and optimization steps reliably recover coherent meshes from imperfect UDFs.

free parameters (1)
  • alpha
    The offset distance that defines the volume whose medial axis is extracted; its specific value or selection rule is not detailed in the abstract.
axioms (1)
  • domain assumption The medial axis of the alpha-offset volume of the UDF corresponds to the desired 0-level set of the original field.
    This is the key insight that allows reuse of mature medial-axis machinery.

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Reference graph

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