BG-Triangle: Bézier Gaussian Triangle for 3D Vectorization and Rendering

CVPR 2025

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, Bézier Gaussian Triangle (BG-Triangle), that combines Bézier 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.

Method

pipeline

Rendering pipeline of BG-Triangles. The BG-Triangle rendering pipeline has three modules. The Primitive Rasterization module tessellates the Bézier triangle, producing coordinate and index maps, as well as boundary points. These maps are then used in the sub-primitive generation module to create pixel-aligned sub-primitives for differentiable rendering. The discontinuity-aware alpha blending module utilizes the boundary points to render images with sharp edges. Finally, the fully differentiable pipeline allows gradient backpropagation along the blue arrows to optimize the control points of BG-Triangles.


Results

results

After training, Bézier primitives effectively outline the object’s silhouette, capturing smooth curves like those in an ellipsoid. The texture is represented by the 3D boundaries, creating recognizable patterns in the boundary map. This structure enables discontinuity-aware rendering, producing sharp, defined edges and superior clarity. In contrast, 3DGS, which aligns only with the pixel sampling rate from training viewpoints, results in blurry close-ups and requires more parameters.

Comparison table

BG-Triangle further leverages attribute sharing within primitives to achieve highly efficient expressiveness, enabling more effective scene representation and novel view synthesis, particularly when using much fewer number of primitives. Our approach demonstrates significant advantages in terms of the LPIPS metric, suggesting that the images we generate are perceptually more similar and visually closer to the target.

Comparisons

Qualitative comparisons.


Please refer to our paper for more results.