PoissonRecon学习笔记

1. Screened Poisson Reconstruction (SPR)

源码：https://github.com/mkazhdan/PoissonRecon
However, as noted by several researchers, it suffers from a tendency to
over-smooth the data. 泊松重建存在过度平滑的现象。
方法：position and gradient constraints are defined over different domain types。集成位置和梯度两类不同域的约束。

与原始泊松相比误差更小，但对噪声敏感！

1.1 Boundary Conditions边界条件

In the original Poisson reconstruction the authors imposed Dirichlet boundary conditions.原泊松重建使用迪利克雷边界条件。
In the present work we extend the implementation to support Neumann boundary conditions as well.扩展诺伊曼边界条件。

As the figure shows, imposing Dirichlet constraints creates a water-tight surface that closes off before reaching the boundary while using Neumann constraints allows the surface to extend out to the boundary of the domain.施加狄利克雷约束会创建一个水密表面，该表面在到达边界之前会关闭，而使用诺依曼约束则允许表面延伸到域的边界。

1.2 运行时间、内存、分辨率对比（顶点数）

Adding a dualized screening term to the Poisson surface reconstruction framework significantly improves its geometric fidelity, while still allowing an efficient multigrid solver.

1.3 Over-Fitting 过拟合

右边screened Poisson更紧密的拟合噪声，所以比右图原始泊松重建质量更低。
At an extreme setting α = 0 we obtain an unscreened Poisson reconstruction as in [Kazhdan et al. 2006].α = 0 时为为筛选的泊松重建，类似于原始泊松重建。

at the base of the Eagle’s neck, derive from our use of a conforming octree. Because we introduce additional leaf nodes near regions of sparse sampling, we obtain a correspondingly refined triangulation at those locations.在鹰脖子的底部，使用一致的八叉树，在稀疏采样区域附近引入了额外的叶节点，所以这些位置获得了相应的细化三角测量。α = 0 时screened Poisson 的细节比原始泊松更丰富。

2. Distributed Poisson Surface Reconstruction

client/server model 服务器/客户端

3. Poisson Surface Reconstruction with Envelope Constraints

出现过拟合表面，多余斑块。
incorporating the depth hull as a Dirichlet constraint within the global Poisson formulation.将深度作为迪利克雷约束，加入全局泊松方程。
Using a visual hull and/or depth hull derived from RGB-D scans to define the constraint envelope. 添加包络约束

3.1 定义隐式曲面

the implicit surface can be defined in regions near the samples, with no isosur-face extracted in regions outside of the support [HDD∗92, FG14].使用紧支持函数，可以在样本附近的区域中定义隐式表面

3.2 网格顶点密度过滤

the implicit surface can be trimmed in a post-processing phase by measuring the sampling density of the input point set at the vertices of the output mesh and discarding subsets of the mesh where the sampling density is too low [Kaz13].测量输出网格顶点处输入点集的采样密度并丢弃采样密度太低的网格子集.

3.3 重建表面位于深度外壳

That is, the reconstructed surface should lie within the object’s depth hull [BGM06] (or equivalently, ray hull [ACCS04]).

4. The Heat Method for Distance Computation开源

热图提高计算效率。并行化处理。
热图计算距离

5. An Adaptive Multi-Grid Solver for Applications in ComputerGraphics

自适应求解器：保证精度的前提下，减少文件容量。

As observed by Agarwala, the offset function should only be high frequency near the seams and can be well-represented using an adaptive quadtree.自适应四叉树。Agarwala 的方法图像拼接方面。
We represent the target gradient field using mixed-degree finite elements stored along (dual) edges.