用可微分的线段近似贝塞尔曲线，实现高效高保真矢量图形重建
CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation
- 用均匀多段线替代贝塞尔曲线最近点求解，几何误差可控在O(S⁻²)
- 在DIV2K和Kodak上比现有方法提升超2dB PSNR，训练速度加快4倍
- 无需额外正则化即可自动剔除无效图元，适合图像重建与参数优化场景
矢量图形因其分辨率无关性、存储紧凑和可直接编辑等优点，使其参数化图元的可微优化成为诱人目标。然而，传统光栅化对几何变化不连续，现有平滑方法随场景复杂度增加需不断引入复杂启发式规则。我们发现这一脆弱性源于梯度权衡：提升前向几何精确性会系统性削弱梯度信号，反之亦然。为此提出CubicSplat，将贝塞尔最近点求解替换为几何误差被严格控制在O(S⁻²)的均匀多段线代理。由此生成的静态计算图天然具备良好条件的梯度，同时通过合成机制实现可见性判断，无需辅助正则化即可剪枝退化图元。在DIV2K和Kodak基准测试中，CubicSplat在闭合填充设置下实现当前最优重建质量，PSNR提升超过2dB，且训练速度相较先前方法快达4倍。代码已公开于https://github.com/CubicSplat/repo。
原文摘要 · Abstract (English)
Vector graphics are prized for their resolution independence, compact storage, and direct editability, making differentiable optimization of their parametric primitives an attractive goal. Yet classical rasterization is discontinuous with respect to geometry, and existing remedies that smooth the forward pass demand increasingly elaborate heuristics as scene complexity grows. We trace this fragility to a gradient seesaw: design choices that improve forward geometric exactness can systematically degrade the induced gradient signal, and vice versa. To navigate this tension we introduce CubicSplat, a differentiable vector rasterizer that replaces Bézier closest-point solvers with uniform polyline surrogates whose geometric error is bounded at $O(S^{-2})$. The resulting static computation graph yields well-conditioned gradients by construction, while a compositing-derived visibility mechanism prunes degenerate primitives without auxiliary regularization. On DIV2K and Kodak benchmarks CubicSplat achieves state-of-the-art reconstruction quality with over 2 dB PSNR gain in the closed-fill setting, while training up to 4x faster than prior methods. The code is available at https://github.com/CubicSplat/repo
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