CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation

2026-08-21

AI Summary

为解决矢量图形优化问题，本文提出CubicSplat方法，通过使用几何误差有界的均匀多段线替代贝塞尔最近点求解器，实现高质量和快速的可微分矢量光栅化。

Abstract

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

Problem

• vector graphics
• rasterization
• discontinuity
• geometric exactness
• gradient signal

Innovation

• differentiable vector rasterization
• uniform polyline surrogates
• geometric error bound
• visibility mechanism