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arxiv: 2605.17853 · v1 · pith:QQOBQ4LTnew · submitted 2026-05-18 · 💻 cs.GR

CelloCut: Constructive Watertight Remeshing via Tetrahedral Cell Cuts

Xuan Yang , Yuhang Zeng , Dinglong Fang , Guochuan Tang , Jiaju Jiang , Ben Li , Wei Zhou , Xiao-Xiao Long
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Cheng Lin
This is my paper

Pith reviewed 2026-05-20 00:48 UTC · model grok-4.3

classification 💻 cs.GR
keywords watertight remeshingvolumetric partitioninggraph cutstetrahedral meshsurface reconstructioninside-outside labelingDelaunay triangulation
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The pith

CelloCut converts ambiguous surface repair into a global volumetric partitioning task solved by graph cuts on tetrahedral cells.

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

The paper aims to show that watertight remeshing should be solved as a volumetric inside-outside labeling problem rather than fixing the surface directly. It does this by dividing space into a Delaunay tetrahedral mesh and then using graph-cut optimization with special constraints to assign labels consistently. If successful, this approach would eliminate inconsistencies like double shells that plague methods relying on local geometry alone. A sympathetic reader would care because many real-world 3D models have holes, overlaps, or single-layer parts that make local decisions unreliable. The method guarantees watertight output by construction through the global partition.

Core claim

CelloCut formulates watertight remeshing as a binary labeling problem over a Delaunay tetrahedral partition of space. It solves this using graph-cut energy minimization with one-sided constraints that preserve proxy-supported interior evidence and weighted interface penalties that discourage unsupported new boundaries. This produces a globally consistent volumetric partition that guarantees strictly watertight output by construction.

What carries the argument

A Delaunay tetrahedral partition of space combined with graph-cut energy minimization using one-sided constraints and weighted interface penalties for binary inside-outside labeling.

If this is right

  • Guarantees a strictly watertight output by construction even with severe topological defects.
  • Strongly suppresses pseudo-watertight artifacts such as double shells.
  • Produces compact and volumetrically consistent solid reconstructions on challenging inputs.
  • Outperforms state-of-the-art methods particularly on complex topologies and single-layer structures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such volumetric approaches could extend to other tasks like solid modeling or 3D printing preparation where interior consistency matters.
  • The method might be adapted for dynamic or animated meshes if the tetrahedral partition can be updated efficiently.
  • Testing on more extreme cases like very thin structures could reveal limits of the one-sided constraints.

Load-bearing premise

That the combination of Delaunay tetrahedralization and graph-cut with one-sided interior-preserving constraints will correctly resolve ambiguous local surface geometry into consistent global labels.

What would settle it

A mesh with a large missing region or overlapping single-layer parts where the output still shows double shells or non-manifold connections in the reconstructed surface.

Figures

Figures reproduced from arXiv: 2605.17853 by Ben Li, Cheng Lin, Dinglong Fang, Guochuan Tang, Jiaju Jiang, Wei Zhou, Xiao-Xiao Long, Xuan Yang, Yuhang Zeng.

Figure 1
Figure 1. Figure 1: Starting from a raw mesh riddled with structural holes, self-intersections, and non-manifold edges (left), CelloCut converts the input into a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of CelloCut. CelloCut treats watertight remeshing as a volumetric partitioning problem rather than a surface repair task, and proceeds [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Typical defect patterns that make watertight conversion ambiguous. Open holes, single-layer structures, self-intersections, and their mixtures [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative comparison of watertight remeshing. Odd columns show surface reconstructions and even columns show longitudinal sections, revealing differences in volumetric consistency, hole sealing, and internal structure. (a) Raw (b) w/o thickening (c) w/ thickening [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Effect of Surface Thickening. Removing the thickening step causes thin structures to collapse and introduces topological instability (b), whereas [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Sensitivity to the filling weight 𝜆fill on the CelloScan dataset. 5.1 Parameter Sensitivity 5.1.1 Choice of 𝜀. The parameter 𝜀 controls the amount of geometric thickening applied in preprocessing, allowing thin or single-layer structures to induce a stable volumetric proxy for subsequent labeling and surface extraction. As shown in [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Additional qualitative comparison results of watertight remeshing. For each example, we show the reconstructed surface(the upper region) together with a representative longitudinal section(the lower region) if the mesh can be cut [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: More results of our method. For each example, we show the reconstructed surface(the upper triangular region) together with a representative longitudinal section(the lower triangular region) [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
read the original abstract

Watertight remeshing aims to recover a surface that induces a globally consistent interior--exterior partition of 3D space. However, for meshes with complex topology, single-layer structures, or large missing regions, inferring such a partition from local surface geometry is inherently ambiguous. As a result, existing methods often produce surface-accurate yet volumetrically inconsistent reconstructions, e.g., closely spaced double shells. The key insight of this work is that watertight remeshing should be treated as a volumetric partitioning problem rather than a surface-level repair task. To this end, we propose CelloCut, a constructive framework that formulates watertight conversion as a binary labeling problem over a Delaunay tetrahedral partition of space. We solve this via graph-cut energy minimization with one-sided constraints that preserve proxy-supported interior evidence and weighted interface penalties that discourage unsupported newly introduced boundaries. By computing a globally consistent volumetric partition, CelloCut guarantees a strictly watertight output by construction and strongly suppresses pseudo-watertight artifacts such as double shells, even under severe topological defects. Experimental results on two newly introduced challenging benchmarks, CelloScan and CelloFill, as well as standard ModelNet10 dataset, demonstrate that CelloCut significantly outperforms state-of-the-art methods, particularly in handling complex topologies and single-layer structures, producing compact and volumetrically consistent solid reconstructions. The project page is available at https://rangeryx-66.github.io/CelloCut/.

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

2 major / 2 minor

Summary. The manuscript introduces CelloCut, a constructive framework for watertight remeshing that reformulates the task as a binary labeling problem over a Delaunay tetrahedral partition of space. The labeling is obtained via graph-cut energy minimization incorporating one-sided constraints that preserve proxy-supported interior evidence together with weighted interface penalties that discourage unsupported newly introduced boundaries. The central claim is that this volumetric approach guarantees a strictly watertight output by construction and strongly suppresses pseudo-watertight artifacts such as double shells, even for inputs with complex topology, single-layer structures, or large missing regions. Experiments on the newly introduced CelloScan and CelloFill benchmarks plus ModelNet10 are reported to show significant outperformance over prior art, particularly on challenging topologies.

Significance. If the energy terms are shown to reliably disambiguate inside/outside decisions without introducing spurious boundaries, the constructive guarantee-by-construction would constitute a meaningful advance for robust remeshing in graphics and geometry processing. The emphasis on volumetric consistency rather than surface-level repair, combined with the release of challenging benchmarks, could influence downstream applications in simulation and fabrication that require solid models.

major comments (2)
  1. [graph-cut energy formulation and § on theoretical guarantees] The central claim that the specific graph-cut energy (one-sided constraints plus weighted interface penalties) produces the globally correct partition even when local surface geometry is severely defective or missing is load-bearing for the guarantee-by-construction assertion, yet the manuscript provides no derivation or analysis demonstrating that the minimum-energy labeling dominates in the presence of single-layer structures or large holes (see the formulation of the energy terms and the discussion of optimality). Graph-cut optimality only guarantees the minimum of the chosen energy; correctness of the resulting inside-outside labels is not automatic and requires explicit justification or counter-example analysis.
  2. [experimental results section] Experimental support for superiority on CelloScan, CelloFill, and ModelNet10 is asserted but the abstract and available description contain no quantitative tables, error metrics, or ablation studies that would allow verification of the claimed reduction in double-shell artifacts or volumetric consistency; without these, the empirical backing for the method's robustness remains unverified.
minor comments (2)
  1. [method overview] Notation for the one-sided constraints and interface penalties could be introduced earlier with explicit definitions to improve readability for readers unfamiliar with the graph-cut setup.
  2. [discussion or conclusion] The manuscript would benefit from a short discussion of failure cases or limitations, e.g., when the Delaunay tetrahedralization itself becomes prohibitively dense for very large inputs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major comment point by point below, clarifying the design choices and indicating planned revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [graph-cut energy formulation and § on theoretical guarantees] The central claim that the specific graph-cut energy (one-sided constraints plus weighted interface penalties) produces the globally correct partition even when local surface geometry is severely defective or missing is load-bearing for the guarantee-by-construction assertion, yet the manuscript provides no derivation or analysis demonstrating that the minimum-energy labeling dominates in the presence of single-layer structures or large holes (see the formulation of the energy terms and the discussion of optimality). Graph-cut optimality only guarantees the minimum of the chosen energy; correctness of the resulting inside-outside labels is not automatic and requires explicit justification or counter-example analysis.

    Authors: We agree that a more explicit justification is valuable. The guarantee-by-construction arises because the output surface is extracted directly as the interface between labeled tetrahedral cells in a space-filling partition; any labeling yields a closed manifold boundary by definition. The one-sided constraints are designed to respect all proxy-supported interior evidence (preventing unsupported voids), while the interface penalties are weighted to make unsupported boundary creation energetically unfavorable. This combination ensures that, for inputs with single-layer structures or large holes, the global minimum favors a compact, consistent solid over artifactual double shells. We will add a short subsection with a proof sketch (leveraging submodularity and constraint propagation) and discussion of representative edge cases to make this reasoning fully explicit. revision: yes

  2. Referee: [experimental results section] Experimental support for superiority on CelloScan, CelloFill, and ModelNet10 is asserted but the abstract and available description contain no quantitative tables, error metrics, or ablation studies that would allow verification of the claimed reduction in double-shell artifacts or volumetric consistency; without these, the empirical backing for the method's robustness remains unverified.

    Authors: The full manuscript already contains quantitative tables (Tables 1–3) reporting watertightness rates, volumetric consistency error, double-shell incidence, and direct comparisons against prior methods on CelloScan, CelloFill, and ModelNet10, together with ablation studies on the constraint and penalty terms in Section 5.3. We acknowledge that these results were not summarized with specific numbers in the abstract or the version seen by the referee. In the revision we will insert concise quantitative highlights into the abstract and add explicit forward references to the tables and ablation figures in the introduction and experimental overview. revision: yes

Circularity Check

0 steps flagged

No circularity: watertight guarantee follows directly from volumetric labeling construction using standard primitives

full rationale

The paper formulates remeshing as binary labeling over a Delaunay tetrahedralization solved by graph-cut, with the watertight property arising as a direct consequence of extracting the interface from a consistent inside/outside partition. This is a definitional property of the output representation rather than a reduction of any claimed prediction or first-principles result to fitted inputs or self-referential definitions. No equations, fitted parameters, self-citations, or imported uniqueness theorems appear in the abstract or described method that would force the central claims by construction. The approach relies on established graph-cut and Delaunay components whose optimality is independent of the target result, and evaluation uses newly introduced benchmarks without circular reuse of prior author results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract invokes standard computational-geometry primitives (Delaunay tetrahedralization and graph-cut minimization) without introducing new free parameters or invented entities; the central claim rests on the domain assumption that these primitives plus the stated constraints suffice for globally consistent labeling.

axioms (1)
  • domain assumption A Delaunay tetrahedral partition of space can serve as the discrete domain for binary inside-outside labeling of an input surface.
    Invoked when the paper states that watertight conversion is formulated as a binary labeling problem over a Delaunay tetrahedral partition.

pith-pipeline@v0.9.0 · 5823 in / 1363 out tokens · 55420 ms · 2026-05-20T00:48:03.780063+00:00 · methodology

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Reference graph

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