We present a method for generating vector graphics, in the form of diffusion curves, directly from noisy samples produced by a Monte Carlo renderer. While generating raster images from 3D geometry via Monte Carlo raytracing is commonplace, there is no corresponding practical approach for robustly and directly extracting editable vector images with shading information from 3D geometry. To fill this gap, we formulate the problem as a stochastic optimization problem over the space of geometries and colors of diffusion curve handles, and solve it with the Levenberg-Marquardt algorithm. At the core of our method is a novel differential boundary element method (BEM) framework that reconstructs colors from diffusion curve handles and computes gradients with respect to their parameters, requiring the expensive matrix factorization only once at the beginning of the optimization. Unlike triangulation-based techniques that require a clean domain decomposition, our method is robust to geometrically challenging scenarios, such as intersecting diffusion curves, and to color noise in the target image, enabling the direct use of noisy Monte Carlo samples without requiring a converged, error-free input image. We demonstrate the robustness and broad applicability of our approach across several test cases. Finally, we highlight several open questions raised by our work, which spans both theory and applications.

翻译：本文提出一种方法，可直接从蒙特卡洛渲染器生成的含噪样本中生成以扩散曲线形式表示的矢量图形。虽然通过蒙特卡洛光线追踪从三维几何生成光栅图像已是常规操作，但目前尚无相应实用方法能够从三维几何中稳健且直接地提取带有着色信息的可编辑矢量图像。为填补这一空白，我们将该问题表述为关于扩散曲线控制点几何与颜色空间的随机优化问题，并采用Levenberg-Marquardt算法进行求解。本方法的核心是一个新颖的微分边界元方法框架，该框架可从扩散曲线控制点重建颜色，并计算其参数梯度，且仅需在优化开始时进行一次昂贵的矩阵分解。与需要洁净区域分解的三角剖分技术不同，本方法对几何挑战性场景（如相交的扩散曲线）和目标图像中的颜色噪声具有鲁棒性，可直接使用含噪的蒙特卡洛样本，无需依赖收敛且无误差的输入图像。我们通过多个测试案例展示了本方法的鲁棒性与广泛适用性。最后，我们重点阐述了本研究在理论与应用层面引发的若干开放性问题。