QEMesh: Employing A Quadric Error Metrics-Based Representation for Mesh Generation

TL;DR

QEMesh addresses mesh generation quality by combining a patch-based PoNQ representation with a latent diffusion model and a multi-decoder VAE to generate PoNQ parameters, guided by an occupancy decoder that selects active voxel cells. The method encodes local geometry via patches with centers, normals, and QEM matrices $Q_i$, enabling detailed yet compact mesh representations and watertight surfaces. The approach demonstrates state-of-the-art-like performance on ShapeNet categories, with strong unconditional generation metrics and robust ablations validating the occupancy mechanism. Overall, QEMesh provides a scalable, geometry-aware framework that improves mesh fidelity and structural integrity for practical 3D content creation.

Abstract

Mesh generation plays a crucial role in 3D content creation, as mesh is widely used in various industrial applications. Recent works have achieved impressive results but still face several issues, such as unrealistic patterns or pits on surfaces, thin parts missing, and incomplete structures. Most of these problems stem from the choice of shape representation or the capabilities of the generative network. To alleviate these, we extend PoNQ, a Quadric Error Metrics (QEM)-based representation, and propose a novel model, QEMesh, for high-quality mesh generation. PoNQ divides the shape surface into tiny patches, each represented by a point with its normal and QEM matrix, which preserves fine local geometry information. In our QEMesh, we regard these elements as generable parameters and design a unique latent diffusion model containing a novel multi-decoder VAE for PoNQ parameters generation. Given the latent code generated by the diffusion model, three parameter decoders produce several PoNQ parameters within each voxel cell, and an occupancy decoder predicts which voxel cells containing parameters to form the final shape. Extensive evaluations demonstrate that our method generates results with watertight surfaces and is comparable to state-of-the-art methods in several main metrics.

Figures (4)

• Figure 1: (Left) Visualization of PoNQ representation on the airplane, in which the Quadric error metric matrix $Q_{i}$ encodes faces of a small surface patch. The patches in different shapes indicate different local geometric information. (Right) We also place some samples from our method at $64^3$ resolution.
• Figure 2: An overview of QEMesh: We show the case where each grid holds only $\textbf{K=1}$ point, normal, and $Q$ matrix. The denoising diffusion step removes the noise to obtain a latent code. Then the parameter decoders convert it to PoNQ parameters (ellipses represent $\hat{v_i}$ and $Q_i$ and arrows represent the normal), and the occupancy decoder produces a mask to select parameters relevant to a shape (green ellipses). To train the occupancy decoder, $D_{occ}$ takes a point $s_i$ and latent features as the inputs to predict whether a cell is occupied by the shape. The blue squares are the features of $s_i$ and its six surrounding points.
• Figure 3: Qualitative evaluation of shape generation at $64^3$ resolution.
• Figure 4: Visual comparison of results from QEMesh with $D_{occ}$ and QEMesh without $D_{occ}$.