Topology-Preserved Auto-regressive Mesh Generation in the Manner of Weaving Silk

TL;DR

A novel mesh tokenization algorithm is proposed that provides a canonical topological framework through vertex layering and ordering, ensuring critical geometric properties including manifoldness, watertightness, face normal consistency, and part awareness in the generated meshes.

Abstract

Existing auto-regressive mesh generation approaches suffer from ineffective topology preservation, which is crucial for practical applications. This limitation stems from previous mesh tokenization methods treating meshes as simple collections of equivalent triangles, lacking awareness of the overall topological structure during generation. To address this issue, we propose a novel mesh tokenization algorithm that provides a canonical topological framework through vertex layering and ordering, ensuring critical geometric properties including manifoldness, watertightness, face normal consistency, and part awareness in the generated meshes. Measured by Compression Ratio and Bits-per-face, we also achieved state-of-the-art compression efficiency. Furthermore, we introduce an online non-manifold data processing algorithm and a training resampling strategy to expand the scale of trainable dataset and avoid costly manual data curation. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

Figures (25)

• Figure 1: Meshes generated by our method. Vertices are colored based on different connected component of mesh. The generated meshes preserve geometric properties (manifoldness, watertightness, consistent face orientation, and part awareness) with state-of-the-art compression ratio.
• Figure 2: Illustration of vertex layering and vertex sorting. Please read the order from right to left. The vertex's layer can be obtained based on the shortest graph distance to starting point $j$, while the vertex ordering algorithm is performed in a manner similar to mathematical induction.
• Figure 3: Illustration of our mesh tokenization algorithm. The mesh vertex for layer $L$ with order $i$ is denoted as $\mathcal{V}^L_i$, its corresponding three types of tokens are denoted as $V_{(L,i)}$, $S_{(L,i)}$, $B_{(L,i)}$, coming from vertex coordinate quantization, self-layer matrix $\mathcal{S}_L$'s compression and between-layer matrix $\mathcal{B}_L$'s compression respectively. The index $(i,j)$ for self-layer matrix $\mathcal{S}_L$ indicates the connection of $\mathcal{V}^L_i$, $\mathcal{V}^L_j$, while the index $(i,j)$ for between-layer matrix $\mathcal{B}_L$ indicates the connection of $\mathcal{V}^L_i$, $\mathcal{V}^{L-1}_j$.
• Figure 4: Difference between our non-manifold processing algorithm to Libigl jacobson2013libigl. Our method performs additional edge structure checking around non-manifold vertex, ensuring surface integrity after edge merging. $\triangle$ denotes the triangle that is ultimately separated.
• Figure 5: Illustration of face normal consistency. Half-edges of layer $L$ are pointing from lower order to higher order, while the layer $L-1$ is opposite.