3D Point Clouds-1

1.概述

表示

注：d11，d12,…可以是法向量，颜色信息

数据来源

激光雷达，RGB-D, CAD models, SFM, 深度图

应用

Robotics， Autonomous driving，Face detection / reconstruction – FaceID Hand pose – Hololens Human pose – Kinect

优点

• 3D information

• Mathematically simple and concise

缺点

• Sparsity
• Irregular – difficulty in neighbor searching
• Lack of texture information
• Un-ordered – difficulty in deep learning
• Rotation equivariance / invariance

2.PCA

Principle Component Analysis

应用

• Dimensionality reduction
• Surface normal estimation
• Canonical orientation
• Keypoint detection
• Feature description

Spectral Theorem

Rayleigh Quotients

利用SVD分析可得到Rayleigh Quotients的结论，以下为证明过程以及SVD的物理意义。U,V代表旋转，特征值代表不同方向的缩放。

3.PCA在点云上的应用

寻找点云主方向

Q: What is the most significant principle component?
A: A direction such that the variance of the projected data points on that direction is maximal
Q: How to get the second significant one?
A: Deflation. Remove the most significant component from the data points, i.e., data point minus the projection. Find the most significant component for the deflated data.
Q: How to get the 3 rd one?
A: Repeat the above steps.

证明

算法流程

Given ???? ???? ∈ ℝ ???? ,???? = 1,2,⋯???? , perform PCA by:

寻找点云法向量

Surface normal：The vector perpendicular to the tangent plane of the surface at a point P

应用

• Segmentation / Clustering
• Plane detection
• Point cloud feature for applications like Deep Learning

算法流程

注：点云在最小特征值所对应特征向量的的方向上投影长度最小；曲率暂时不知道怎么应用

考虑噪声

在选择neighbors过程中，如果半径过大，法向量会受到不相关点的影响，如果半径过小，法向量受到噪声影响变大。
解决办法：
• Weighted based on other features

a. Lidar intensity
b. RGB values
• RANSAC
• Deep Learning

以上为学习过程记录，如有错误，请多指教。