Q-REG
Jin, S., Barath, D., Pollefeys, M., & Armeni, I. (2023). Q-REG: End-to-End Trainable Point Cloud Registration with Surface Curvature.
- paper: 2309.16023v1] Q-REG: End-to-End Trainable Point Cloud Registration with Surface Curvature (arxiv.org)
- code: waiting
Questions Raised
- RANSAC-like estimation methods cope with the combinatorics of the problem via selecting random subsets of m correspondences( e.g., m=3 for rigid pose estimation). this allows to progressively explore the \((\frac{n}{m})\) possible combinations, where n is the total number of matches.
简单来说就是RANSAC style不可微，不能end-to-end；而其他learning-based方法为了实现端到端就将hard correspondence换成了基于socre的soft correspondence(hard就是True or False，soft就是有权重，或者说点对匹配程度)，又会使得计算开销太大，并且引入大量噪声。
作者就想实现hard correspondence的端到端，怎么办，采用single correspondence来预测变换就可以了，这样就没有random subsets，而是迭代遍历correspondence set，取最好预测结果。
Contribution
- 设计了Q-REG，一种结合single correspondence的local surface patches(fitting quadrics)，来估计位姿的点云配准方法，意图替代RANSAC。从介绍上，Q-REG与correspondence matching method 无关(it is agnostic to the correspondence matching method)，并且能够快速做outlier rejection by filtering degenerate solutions and assumption inconsistent motions (rigid poses inconsistent with motion priors (e.g., to avoid unrealistically large scaling).)
- 将Q-REG设计成可微(differentiable)方案，用于无论是在correspondence matching method 还是 pose estimation method的端到端训练
- 刷SOTA哩
Description
employing higher-order geometric information , Q-REG achieving exhaustive search to replace RANSAC and improve the performance and run-time
First Step: Correspondence Matching
使用任意Correspondence Matcher（e.g patch-based: PPFNet, PPF-FoldNet; full-conv: FCGF）得到feature-matching based putative correspondences \(\{P, Q\}\in C\) , 用于之后的Q-REG方法预估变换矩阵。
Q-REG是single-correspondence方法，因此区别于RANSAC每次随机挑选三对corresponding point \(\{p, q\}\) 预测变换矩阵，Q-REG每次只取单对corresponding point，用于estimate transform between \(P\) and \(Q\) 。
Second Step: Q-REG
Q-REG直接当作工具用的步骤为：
- 从correspondence set \(C\) 中迭代取出single correspondence \(\{p,\ q \}\) ;
- 对以每个single corrspondence为输入预测变换矩阵
- 选择best transformation model 作为初步结果, the pose quality metric is calculated as the cardinality of its support i.e., the number of inliers.
- 之后根据论文[^ 1] 的方法进行local optimization.( a local re-sampling and re-fitting of inlier correspondences based on their normals (coming from the fitted quadrics) and positions. )
如果嵌入端到端训练则只进行到第二步时根据预测结果构建Loss: \(L_{pose}\) 。
后文对single correspondence为输入预测变换矩阵的过程进行详述，以及介绍 \(L_{pose}\) 的构成
1. Quadric Fitting based local patch
对于single correspondence \(\{p, q\}\in C\) ，可以为点划分local patch(Q-REG通过K=50的KNN来划分)，预测一对local patch，并计算两个loca patch彼此的LRF(local reference frame) \(R_p, R_q \in SO(3)\) （即作为将点从世界坐标系转换到局部参考系的旋转矩阵）。假如预测正确，我们就可以做两片点云的对齐( \(R=R_qR_p^T\) )。因此Q-REG应用二次曲面拟合来预估 \(R_p,\ R_q\) 。
至于translation vector \(t\) ，论文直接以 q, p作为两片点云重叠区域的质心， \(t=q-p\) 。
论文中应用如下约束拟合3D quadric surface：
\[\hat{p}^TQp=0 \]- \(\hat{p}\) ：3D homogeneous point(3D齐次点) lying on the surface
- Q is the quadirc parameters in matrix as:
理论上最佳的是local patch的所有点都能落在曲面上，但是当然不可能
标签：correspondence,论文,矩阵,patch,single,阅读,local,REG From： https://www.cnblogs.com/name555difficult/p/17742819.html