NDT algorithms and some common registration algorithms

Original link: http://ghx0x0.github.io/2014/12/30/NDT-match/

In the present three-dimensional registration with more is the ICP iterative algorithm, need to provide a good initial value, and due to the shortcomings of the algorithm itself, the final iteration results may fall into the local optimal. This article introduces another kind of better registration algorithm, NDT registration. This registration algorithm is time-consuming and stable, relative to the initial value is small, the initial value error is large, can also be well corrected.

Introduction:

• Sampling:
  • 3d point cloud data in the vicinity of the camera near the cloud density, the distance density is small, so in the next sampling using a unified sampling method or will retain the density is uneven;
    One way to do this is to divide the space into squares, and the point clouds in each lattice are randomly picked up, and the points are sufficient.
  • Short wave will produce higher resolution and less specular reflection. The use of multiple depth cameras can create crosstalk problems, especially when specular reflection is severe.

Cameras that can capture image depth:

1. Radar Radio
2. LiDAR LiDAR
   • Triangular measurement method
   • Tof Flight Time Method
   • Phase Difference method
3. Sonar
4. Binocular Vision
   • Binocular vision is a passive triangulation measurement;
     Disadvantages:
     A Binocular vision only can be detected by the feature points to detect the depth, in the low-contrast environment, only a few feature points can be detected;
     B Another disadvantage of binocular vision is that the distance between two cameras is increased, the depth accuracy is reduced, and the blind area increases, mainly for long distance measurements of several meters away.
     C No texture is detected on the surface.
5. Triangulation Measurement of projection light
6. Tof Depth Camera
   • is actually measured by the phase offset method;
     Tof depth camera compared to LiDAR's tof is fast acquisition speed, hardware cheap
     The disadvantage is that the noise is obvious and needs to be calibrated and affected by the outside light and the active light itself. And the exposure time is not easy to determine

View matching (registration):

1. Icp
   Disadvantages:

   C．每次迭代都要搜索最近点，计算代价高昂

   There are a variety of optimized variant algorithms, such as eight-fork tree, etc.
2. Idc

    ICP的一种改进，采用极坐标代替笛卡尔坐标进行最近点搜索匹配

3. Pic

    考虑了点云的噪音和初始位置的不确定性

4. point-based Probabilistic Registration

    需要首先建立深度图的三角面片

5. ndt--Normal Distribution Transformation:

    计算正态分布是一个一次性的工作（初始化），不需要消耗大量代价计算最近邻搜索匹配点    概率密度函数在两幅图像采集之间的时间可以离线计算出来  

6. Gaussian fields

    和NDT正态分布变换类似，利用高斯混合模型考察点和点的距离和点周围表面的相似性

7. Quadratic patches
8. Likelihood-field matching--with airport matching
9. CRF Matching

    缺点： 运行速度慢，在3d中实时性能不好，误差大。

10. Branch-and-bound Registration
11. Registration using local geometric features

NDT algorithms:

1. Divides the space (reference scan) into individual lattice cells
2. Vote the point cloud into each lattice

3. Calculate the normal distribution of a grid PDF parameter

4. Change each point of the second scan by the transformation of the transfer matrix T

5. The second scan points to which lattice of reference, and calculates the probability distribution function of the response

6. To find the optimal value of all points, the objective function is

PDF可以当做表面的近似表达，协方差矩阵的特征向量和特征值可以表达表面信息（朝向、平整度）格子内少于3个点，经常会协方差矩阵不存在逆矩阵，所以只计算点数大于5的cell，涉及到下采样方法。

• Optimization of NDT:
  Lattice parameters are the most important, too large to make the accuracy is not high, too small cause memory is too high, and only two images of a small difference in the case to match

1. Fixed size
2. Eight fork tree build, lattice have big small
3. iterations, using finer squares each time
4. K Clustering, how many classes there are the number of cells, lattice size varies
5. Linked-cell
6. Three-line interpolation smooths adjacent lattice cells resulting in discontinuities, improving accuracy
   Cons: Interpolation causes time to be 4 times times normal
   Pros: Can improve robustness

ICP algorithm:

1. Given reference point set p and data point set Q (when given initial estimated RT)
2. Each point in the q is searched for the corresponding nearest point in P, which constitutes a matching point pair
3. Finding Euclidean distance and error objective function errors for matching point pairs
4. Using SVD decomposition to find R and T, so that the error is minimized
5. Change Q according to R and T, and use this as the benchmark to return to 1 to re-find the corresponding point pair

NDT 耗时稳定，跟初值相关不大，初值误差大时，也能很好的纠正过来；  ICP耗时多，容易陷入局部最优；  可以根据格子cell的PDF的协方差矩阵计算特征向量特征值，每个格子有球形状、平面、线型三种类型，根据朝向作以统计，得到局部或者一幅图像的特征直方图  

The article comes from Martin Magnusson the three-dimensional normal-distributions transform-an efficient representation for Registration,surface analysis, and Loop Detection. The author introduces in detail the registration effect of NDT under various conditions and the detailed experimental comparison with other registration methods, and uses the NDT algorithm to register the three-dimensional scene in the mine hole and complete the slam task.

NDT algorithms and some common registration algorithms