BG-Triangle: B'ezier Gaussian Triangle for 3D Vectorization and Rendering

2025-03-18

AI Summary

Existing differentiable rendering methods struggle to preserve geometric boundary sharpness. To address this, we propose BG-Triangle—a hybrid primitive representation that unifies Bézier triangles (explicit, resolution-independent vector boundaries) with anisotropic Gaussians (probabilistic surface modeling), enabling boundary-aware 3D vectorized modeling and rendering. Our method introduces three key components: discontinuity-aware differentiable rasterization, boundary gradient correction, and adaptive primitive densification and pruning. Experiments demonstrate that our approach achieves rendering quality comparable to 3D Gaussian Splatting (3DGS), while significantly improving boundary crispness. It reduces primitive count by one to two orders of magnitude, supports lossless scaling, and yields compact vector scene representations. This establishes a new paradigm for high-fidelity, editable neural vector rendering.

Technology Category

• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Differentiable rendering enables efficient optimization by allowing gradients to be computed through the rendering process, facilitating 3D reconstruction, inverse rendering and neural scene representation learning. To ensure differentiability, existing solutions approximate or re-formulate traditional rendering operations using smooth, probabilistic proxies such as volumes or Gaussian primitives. Consequently, they struggle to preserve sharp edges due to the lack of explicit boundary definitions. We present a novel hybrid representation, B'ezier Gaussian Triangle (BG-Triangle), that combines B'ezier triangle-based vector graphics primitives with Gaussian-based probabilistic models, to maintain accurate shape modeling while conducting resolution-independent differentiable rendering. We present a robust and effective discontinuity-aware rendering technique to reduce uncertainties at object boundaries. We also employ an adaptive densification and pruning scheme for efficient training while reliably handling level-of-detail (LoD) variations. Experiments show that BG-Triangle achieves comparable rendering quality as 3DGS but with superior boundary preservation. More importantly, BG-Triangle uses a much smaller number of primitives than its alternatives, showcasing the benefits of vectorized graphics primitives and the potential to bridge the gap between classic and emerging representations.

Problem

• Achieve sharp edge preservation in differentiable rendering
• Reduce uncertainties at object boundaries during rendering
• Bridge gap between classic and emerging 3D representations

Innovation

• Combines Bézier triangles with Gaussian models
• Uses discontinuity-aware rendering for boundaries
• Employs adaptive densification and pruning scheme