基于变分的图法向积分
Variational Graph-based Normal Integration
把法向积分从规则网格推广到非结构化点集，用有向加权图 + 双分量高斯混合后验显式建模深度不连续，可直接用于散乱点云/稀疏采样的表面重建与深度补全。
原文依据 we construct a directed, weighted graph that jointly parameterizes the surface geometry and pairwise point correlations
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论我们提出一个通用的、基于优化的保深度法向积分框架。与现有在规则网格上定义表面朝向的方法不同，我们的方法引入统一的图表述，能够对非结构化域上的半可微表面进行积分。给定从某一表面均匀采样得到的一组点，我们构建一个有向加权图，该图联合参数化表面几何与点对相关性。通过最小化图中投影的点到平面距离来恢复表面深度，并借助变分推理实现该目标。在我们的表述中，估计的表面法向作为潜变量，通过双分量高斯混合的后验概率编码局部几何，从而使深度不连续能够由采样的三元组配置显式推断。未知量以交替方式估计，并且我们通过将该推理过程与形状变形相关联，给出了其几何解释。实验结果表明，所提方法不仅在规则网格数据上取得更优性能，还能有效泛化到散乱点，而现有方法无法直接支持这一情形。
英文原文摘要 1288 字符
We present a general optimization-based framework for depth-preserving normal integration. Unlike existing methods that operate on surface orientations defined over regular grids, our approach introduces a unified graph-based formulation capable of integrating semi-differentiable surfaces on unstructured domains. Given a set of points uniformly sampled from a surface, we construct a directed, weighted graph that jointly parameterizes the surface geometry and pairwise point correlations. Surface depth is recovered by minimizing projected point-to-plane distances across the graph, and we attain this objective through variational inference. In our formulation, estimated surface normals serve as latent variables that encode local geometry via the posterior probabilities of a two-component Gaussian mixture, allowing depth discontinuities to be explicitly inferred from sampled triplet configurations. The unknowns are estimated in an alternating fashion, and we provide a geometric interpretation of this inference process by relating it to shape deformation. Experimental results show that the proposed method not only delivers superior performance on regularly gridded data, but also generalizes effectively to scattered points, which existing approaches do not directly support.