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.

翻译：可微渲染通过允许在渲染过程中计算梯度，促进了三维重建、逆向渲染与神经场景表示学习，从而实现高效优化。为确保可微性，现有解决方案使用平滑的概率代理（如体素或高斯基元）来近似或重新表述传统的渲染操作。因此，由于缺乏显式的边界定义，这些方法难以保持锐利边缘。我们提出了一种新颖的混合表示方法——贝塞尔高斯三角形（BG-Triangle），它将基于贝塞尔三角形的矢量图形基元与基于高斯的概率模型相结合，在实现分辨率无关的可微渲染的同时，保持精确的形状建模。我们提出了一种鲁棒且有效的非连续性感知渲染技术，以减少物体边界处的不确定性。我们还采用了一种自适应致密化与剪枝方案，以在可靠处理细节层次（LoD）变化的同时实现高效训练。实验表明，BG-Triangle 在达到与 3DGS 相当的渲染质量的同时，具有更优的边界保持能力。更重要的是，BG-Triangle 使用的基元数量远少于其他替代方案，这展示了矢量化图形基元的优势以及弥合经典表示与新兴表示之间差距的潜力。