用自适应三角网格重构法，让法向积分更快更省内存。
An Adaptive Screen-Space Meshing Approach for Normal Integration
- 根据法向计算曲率，自动聚类像素成三角形网格。
- 相比像素网格，顶点数减少10至100倍，运行时间近似线性以下。
- 适合需要快速处理高分辨率法向图的三维重建场景。
从法向量重建表面是光度立体的核心步骤。本文提出在图像域中进行自适应表面三角化，随后在三角网格上执行法向积分。关键思路是通过法向量计算曲率，识别平坦区域并聚合像素形成三角形。通过单一用户参数控制逼近精度，实现从低到高分辨率网格的无缝生成。与像素网格相比，该三角网格能局部适应表面细节，支持更稀疏表示。新提出的基于网格的法向积分公式严格源于离散微分几何，导出良态线性系统。真实与合成数据实验表明，所需顶点数仅为像素数的1/10至1/100。实验显示此稀疏性带来顶点数的亚线性运行时间。对于6400万像素的法向图，本方法可在分钟级完成网格生成与积分，而传统像素方法仅积分就需数小时。
原文摘要 · Abstract (English)
Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is that surface curvature can be computed from normals. Based on the curvature, we identify flat areas and aggregate pixels into triangles. The approximation quality is controlled by a single user parameter facilitating a seamless generation of low- to high-resolution meshes. Compared to pixel grids, our triangle meshes adapt locally to surface details and allow for a sparser representation. Our new mesh-based formulation of the normal integration problem is strictly derived from discrete differential geometry and leads to well-conditioned linear systems. Results on real and synthetic data show that 10 to 100 times less vertices are required than pixels. Experiments suggest that this sparsity translates into a sublinear runtime in the number of pixels. For 64 MP normal maps, our meshing-first approach generates and integrates meshes in minutes while pixel-based approaches require hours just for the integration.
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