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VertexRegen: Mesh Generation with Continuous Level of Detail

Conference: ICCV 2025 arXiv: 2508.09062 Code: Project Page Area: 3D Vision Keywords: Mesh Generation, Progressive Meshes, Continuous Level of Detail, Autoregressive, Vertex Split

TL;DR

VertexRegen is proposed to reframe mesh generation—inspired by progressive meshes—as learning the inverse of edge collapse, i.e., vertex split, enabling "anytime" mesh generation with continuous level of detail.

Background & Motivation

Fundamental limitations of existing autoregressive mesh generation methods (MeshGPT, MeshXL, etc.): - Part-to-complete generation paradigm: intermediate steps yield incomplete meshes (missing faces) - No detail control: the full sequence must be completed to obtain a valid mesh - Early stopping = missing faces, not a lower-resolution mesh

VertexRegen's innovation: a coarse-to-fine generation paradigm where every intermediate step produces a valid mesh, differing only in level of detail.

Method

Progressive Meshes Review

Two invertible operations: - Edge collapse \(\text{ecol}(v_s, v_t)\): merges two adjacent vertices, removing two faces and one vertex - Vertex split \(\text{vsplit}(v_s, v_l, v_r, v_t)\): the inverse operation, restoring a vertex and two faces

Progressive mesh representation: \(\text{PM}(\mathcal{M}) = (\mathcal{M}_0, \{\text{vsplit}_0, \cdots, \text{vsplit}_{n-1}\})\)

The edge collapse ordering is determined by QEM (Quadric Error Metrics).

VertexRegen Serialization

Complete sequence: 

M: [<bos>, [M_0 sequence], <sep>, [vsplit_0], ..., [vsplit_n-1], <eos>]

Base mesh \(\mathcal{M}_0\) tokenization: follows the MeshXL scheme (9 tokens per face), but encodes only an extremely coarse initial mesh (averaging 18 faces vs. 457 in the original).

Vertex split tokenization: leverages the half-edge data structure to resolve ambiguity; each operation requires recording only four vertices \(v_s, v_l, v_r, v_t\) (12 tokens, or 10 tokens in boundary cases).

Key Role of the Half-Edge Data Structure

Vertex split requires determining which half of the one-ring neighborhood of \(v_s\) belongs to \(v_t\). By traversing half-edges from \(\mathcal{H}_{ls}^1\) to \(\mathcal{H}_{\cdot s}^r\), the partition is precisely determined:

\[\{v_k | \mathcal{H}_{\cdot s}^k, k \neq r\} = N_{k+1}(v_s) - \{v_l, v_r, v_t\}\]

Guided Decoding

A state machine is maintained to execute vertex splits at runtime. Enforced constraints: - \(v_s\) must be a vertex in the current mesh - \((v_s, v_l)\) and \((v_s, v_r)\) must be valid edges - Only one of \(v_l\) or \(v_r\) is permitted to be <nil>

Key Experimental Results

Unconditional Mesh Generation

Method Tokenization COV↑ MMD↓ 1-NNA (%) JSD↓
MeshXL Flattened coords 51.76 8.30 50.84 3.81
MeshAnything V2 AMT 50.33 8.50 52.25 4.84
EdgeRunner EdgeBreaker 51.39 7.81 49.44 3.22
VertexRegen Progressive 51.03 8.29 50.22 2.89

VertexRegen achieves generation quality comparable to SOTA while uniquely supporting continuous level of detail. It achieves the best JSD, indicating that the generated distribution more closely matches the reference distribution.

Face-Constrained Generation (@400 Faces)

Method COV↑ MMD↓ 1-NNA
MeshXL (w/ FCC) 41.20 10.03 59.06
VertexRegen 50.92 8.31 51.03

VertexRegen substantially outperforms baselines under low face-count constraints, as its coarse-to-fine generation preserves complete structure throughout.

Compression Efficiency

Method Compression Ratio
MeshXL 1.0
MeshAnything V2 0.46
EdgeRunner 0.47
VertexRegen (w/ HE) 0.73
VertexRegen (w/o HE) 0.89

The half-edge data structure reduces sequence length by 22%.

Highlights & Insights

  1. Paradigm shift: from "part-to-complete" to "coarse-to-fine," fundamentally transforming the properties of mesh generation
  2. Elegant use of the half-edge data structure: resolves neighborhood assignment ambiguity in vertex splits
  3. Anytime generation: stopping at any point yields a valid mesh
  4. Inherited theoretical guarantees from progressive meshes: each vertex split is a deterministic inverse operation

Limitations & Future Work

  • The base mesh \(\mathcal{M}_0\) still requires MeshXL-style generation, accounting for 5.68% of the total sequence length
  • Compression efficiency (0.73) is inferior to AMT (0.46), as vertex splits require four vertices
  • Predicting an invalid vertex split interrupts the chain of generation
  • Guided decoding requires maintaining a state machine, increasing inference complexity
  • MeshGPT, MeshXL: autoregressive mesh generation
  • Progressive Meshes (Hoppe): theoretical foundation for progressive meshes
  • EdgeRunner: EdgeBreaker compression-based tokenization

Rating

  • Novelty: ⭐⭐⭐⭐⭐ (an elegant integration of progressive meshes and generative models)
  • Technical Depth: ⭐⭐⭐⭐⭐ (sophisticated design of half-edge data structure and guided decoding)
  • Experimental Thoroughness: ⭐⭐⭐⭐ (unconditional + conditional + ablation)
  • Value: ⭐⭐⭐⭐⭐ (continuous LOD addresses a genuine practical need)