用预设法向量指导几何去噪，提升表面细节恢复能力。
Geometry Denoising with Preferred Normal Vectors
- 基于预设法向量集合构建分割与正则化，实现形状自适应去噪
- 通过二阶形状微分更新顶点，有效保留几何结构特征
- 适用于文物等复杂曲面的高保真修复，尤其适合低噪声场景
我们提出一种基于表面法向量先验知识的几何去噪新范式。该先验以一组预设法向量（称为标签向量）的形式存在，去噪过程自然嵌入分割任务——依据顶点法向量与标签向量集的相似性进行划分。通过总变差项实现正则化，采用分裂Bregman（ADMM）方法求解优化问题。顶点更新步骤基于二阶形状微分。实验包括一座风化严重的中世纪墓碑铭文的去噪处理，验证了方法在保留精细结构方面的有效性。
原文摘要 · Abstract (English)
We introduce a new paradigm for geometry denoising using prior knowledge about the surface normal vector. This prior knowledge comes in the form of a set of preferred normal vectors, which we refer to as label vectors. A segmentation problem is naturally embedded in the denoising process. The segmentation is based on the similarity of the normal vector to the elements of the set of label vectors. Regularization is achieved by a total variation term. We formulate a split Bregman (ADMM) approach to solve the resulting optimization problem. The vertex update step is based on second-order shape calculus. We present various examples including the denoising of an eroded medieval gravestone inscription.
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