通过多方向法曲率惩罚实现图像与表面平滑，保留锐利边缘。
Total Normal Curvature Regularization and its Minimization for Surface and Image Smoothing
- 基于多方向法曲率的正则化新方法
- 能保持边缘清晰且具备各向同性特性
- 无需复杂调参，适合图像/表面处理任务
我们提出一种新的曲率正则化方法，通过惩罚多个方向的法曲率来实现。该总法曲率正则化能生成具有锐利边缘和精确各向同性特性的解。为解决由此产生的高阶非线性优化问题，我们将其重构为一个时变偏微分方程（PDE）系统的稳态解求解问题。时间离散采用算子分裂法，每个分数步的子问题要么有闭式解，要么可用高效算法快速求解。该方法避免了复杂的参数调优，对参数选择具有强鲁棒性。在表面与图像平滑问题中，该方法的效率与有效性已得到严格验证。
原文摘要 · Abstract (English)
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic properties. To tackle the resulting high-order nonlinear optimization problem, we reformulate it as the task of finding the steady-state solution of a time-dependent partial differential equation (PDE) system. Time discretization is achieved through operator splitting, where each subproblem at the fractional steps either has a closed-form solution or can be efficiently solved using advanced algorithms. Our method circumvents the need for complex parameter tuning and demonstrates robustness to parameter choices. The efficiency and effectiveness of our approach have been rigorously validated in the context of surface and image smoothing problems.
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