CelloCut: Constructive Watertight Remeshing via Tetrahedral Cell Cuts

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/.

• The paper introduces CelloCut, a volumetric partitioning framework that ensures watertight remeshing of defective triangle meshes.
• CelloCut uses tetrahedral cell cuts guided by thickened proxy surfaces and global optimization to resolve mesh defects and ambiguities.
• Empirical analysis demonstrates CelloCut's superiority in producing strictly watertight outputs across standard benchmarks, outperforming competing methods.

CelloCut: Constructive Watertight Remeshing via Tetrahedral Cell Cuts

Problem Formulation and Motivation

CelloCut addresses the challenge of watertight remeshing for defective triangle meshes, a task critical for downstream applications ranging from physical simulation to generative model training. The paper articulates that standard mesh repair and surface reconstruction methods fail to enforce global interior-exterior consistency, especially when faced with complex topology, single-layer geometries, or substantial missing regions. Such defects transform watertight conversion from a surface restoration task into an intrinsically ambiguous volumetric partitioning problem—where the objective must shift from replicating local geometry to inferring a compact, globally consistent solid interpretation.

The authors explicitly distinguish their approach from classical surface-based mesh repair, which cannot resolve ambiguities resulting from defects like holes, self-intersections, and near-zero-thickness structures. Instead, CelloCut leverages volumetric evidence, guided by a thickened proxy and global optimization, as the basis for robust watertight completion.

Algorithmic Framework

CelloCut operates in three algorithmic stages:

1. Surface Thickening and Volumetric Embedding: The input mesh is embedded into a volumetric domain via a thickened Unsigned Distance Field (UDF). Marching Cubes is employed to extract a robust proxy surface, which is then decimated for efficient processing. Delaunay tetrahedralization constructs an adaptive volumetric discretization, enabling fine geometric detail and numerical stability.
2. Binary Volumetric Partitioning via Graph Cut:

The volumetric domain is partitioned by solving a constrained binary labeling problem over tetrahedral cells. The optimization is fundamentally asymmetric: - Unary Term (One-Sided Anchoring): Interior cells supported by the thickened proxy are strictly preserved, preventing erosion of reliable interior mass and suppressing double-shell artifacts. - Pairwise Term (Fill-Aware Regularization): Interface penalties are weighted to discourage unsupported new boundaries, biasing solutions towards compact, single-shell completion. The filling weight $A_{\text{fill}}$ tunes the aggressiveness of hole filling.

The max-flow/min-cut paradigm is adopted for global optimization. This approach ensures that the output is strictly watertight by construction rather than relying on fragile local consistency heuristics.

1. Surface Extraction and Refinement: The optimized volumetric partition yields a boundary, which is extracted and further regularized as a Signed Distance Field. Marching Cubes reconstructs the final watertight surface at high resolution, while decoupling geometric refinement from topological guarantees.

Experimental Analysis

Robustness, geometric fidelity, and perceptual quality are exhaustively evaluated on ModelNet10, the newly curated CelloScan, and CelloFill benchmarks:

• ModelNet10 Robustness:

CelloCut produces strictly watertight outputs with no open boundaries, no non-manifold entities, and zero failures across all models. Competing algorithms such as fTetWild and Craftsman exhibit boundary violations, while methods like VolumeMesher fail on vertex-manifoldness.

• CelloScan Geometric Metrics:

On scans with severe defects, CelloCut achieves the lowest Chamfer Distance (CD: 0.000048), highest Absolute Normal Consistency (ANC: 0.9452), and top F1 score ([email protected]: 96.96%), outperforming ManifoldPlus, Dora, and fTetWild. The benchmarking protocol discards the defective input as reference and instead uses virtual scanning to assess fidelity to an externally observable boundary, exposing the volumetric consistency of CelloCut’s reconstructions.

• CelloFill Perceptual Metrics:

Under large missing regions, CelloCut attains the lowest FID (20.17), competitive LPIPS (0.0465), and high CLIP score (98.42). These results validate that the method reconstructs visually coherent and semantically consistent solids, unlike MeshFix and grid-based methods that frequently fail to deliver watertight outputs.

Qualitative comparisons further demonstrate CelloCut’s capacity to resolve intricate defects (holes, self-intersections) and reconstruct compact, artifact-free solids suitable for downstream 3D pipelines.

Ablation Study and Parameter Sensitivity

A comprehensive ablation study isolates the necessity of surface thickening and the asymmetric unary term:

• Surface Thickening:

Removing thickening collapses thin structures and destabilizes volumetric partitioning, resulting in drastic loss of fidelity and topological stability.

• Unary Constraints:

Eliminating the unary term leads to degenerate solutions lacking extractable interior-exterior partitions, reaffirming its anchoring role.

• Filling Weight ($A_{\text{fill}}$):

Aggressive hole filling (low $A_{\text{fill}}$) creates excessive new surfaces, degrading geometry; high values suppress completion but ensure volumetric compactness. Default settings yield optimal balance.

Mesh simplification prior to tetrahedralization robustly preserves geometric accuracy while dramatically reducing computational overhead. Runtime profiling reveals that graph-cut optimization dominates total processing time, motivating future work in parallelized solvers and adaptive discretization.

Implications and Future Directions

Practically, CelloCut’s guarantees are pivotal for simulation-ready asset generation, watertight model training for generative pipelines, and robust computational fabrication. Theoretically, the volumetric partitioning paradigm offers a structured methodology for resolving inherent ambiguities in defective mesh inputs, enabling globally consistent completion that surface-based approaches cannot achieve.

Current limitations center on efficiency, as global volumetric optimization is computationally intensive. Another limitation is the uniform solidification assumption; future directions may integrate semantic priors or user-guidance for mixed solid-shell reasoning, leveraging advances in learned volumetric labeling for even greater robustness and versatility.

Integration with learning-based shape analysis and generative models could further enhance CelloCut, enabling context-aware completion in highly ambiguous regions and opening the door for real-time remeshing pipelines.

Conclusion

CelloCut "Constructive Watertight Remeshing via Tetrahedral Cell Cuts" (2605.17853) establishes a volumetric partitioning framework for watertight mesh conversion, backed by strong theoretical guarantees and demonstrable empirical superiority. The methodology transforms defective inputs into simulation-ready solids, robustly resolving ambiguous volumes while maintaining geometric fidelity and visual quality. The approach redefines the core of mesh repair by shifting from local surface edits to global volumetric reasoning, laying the foundation for future advances in scalable and semantics-aware remeshing.