Clean up the draft box , I forgot to release what I wrote long ago ;）

1. Summary

1.1 original text

subject ：SO-Net：Self-Organizing Network for Point Cloud Analysis, CVPR2018
The paper ：https://link.zhihu.com/?target=https%3A//arxiv.org/abs/1803.04249
Code ：https://github.com/lijx10/SO-Net
brief introduction ： The self-organizing neural network is mainly used （SOM) To get representative points

1.2 Background knowledge

Self organizing neural network （SOM）
Kohonen A neural network model is proposed , Data can be Unsupervised learning clustering .
Contains only ： Input layer + Output layer （ Mapping layer ）, Because there is no middle hidden layer , Therefore, the output maintains the original topology .

SOM It is an unsupervised clustering method , Simulate the different characteristics of the division of labor of nerve cells in different regions of the human brain , That is, different regions have different corresponding characteristics , And automatically complete . The problem of identifying the unknown cluster center can be realized by self-organizing map .

Training uses “ Competitive learning “ The way , Each input sample finds a node in the hidden layer that best matches it , be called ”winning neuron“. Then the random gradient descent method is used to update the activation node parameters . meanwhile , The points adjacent to the active node also update the parameters appropriately according to their distance from the active node .

SOM There are mainly two steps ：

1. Select the active node ;
2. Update the weights of the active points and adjacent nodes ;
   –> Brain science research shows that ： Adjacent neurons can stimulate each other , thus SOM The operation is similar ;
   –> Determine the neighborhood ： Set a radius , All points within the radius are adjacent points , As learning progresses , Make the radius smaller and smaller until the end of learning .

SOM effect ： clustering & Dimension reduction

2. motivation

And PointNet++ And PointCNN The overall idea is similar , Lower level or PointNet, namely ： First select some representative points , Partition the point cloud , And then use PointNet, adopt Max-pooling Each region gets a trait vector as a node feature , Then splice all node features , Receive FC Classification in layers .

The difference ： Selecting the center point is through self-organizing structure mapping SOM To carry out , And only one down sampling operation .

3. thought

• Build self-organizing structure mapping （SOM） To choose representative points , To establish the spatial distribution of point clouds .
• The network has a multi-level structure
• The receptive field can pass through KNN To adjust

4. Algorithm

Self organizing networks ： In a point cloud N Point use M individual SOM Node to represent .

4.1 SOM Permutation invariance of

In this article SOM The size is set to $m\times m$ size , among $m\in [5,11]$. Compared with the feedback mechanism in the network ,SOM It's unsupervised contrastive learning .

however SOM Not permutable , because ：
（1） The training results are highly dependent on the initialization node ;
–> Fixed number of initialized nodes , It can be homogenized and dispersed in a unit ball to obtain the initialization point , Pictured 2（a） Shown
（2） The update per sample depends on the sorting of the input points ;
–> Not applicable to point by point update , Use Block update , That is, the gain of accumulating all points is updated , Avoid permutation changes introduced by sequence ;

4.2 Coding framework

SOM Is to guide hierarchical feature extraction , And a tool for systematically regulating the overlap of receptive fields .

Given SOM Output , For each node $s_i$ Look for it K Nearest neighbor ：

Then put each $p_i$ Subtract from related nodes , Owned by one becomes $k$ A little bit :

such KN A normalized point is passed forward to the next layer ：

Finally, the feature extraction of nodes uses the maximum pool to extract $KN$ A point feature becomes $M$ A node feature .

Since each point is normalized to $k$ A coordinate , It also guarantees $M$ The receptive fields cover each other after the maximum pool , That is to say $M
$individualspotcapsuleenclosed了$kN$individualreturnOneturnspot,thisinOf$k$ Is a parameter that controls coverage .

and SOM Similar feature aggregation . Because the input point of the first layer is from $M$ individual SOM Nodes represent , So it's actually divided into $M$ A mini point cloud , Pictured 3 Shown . Every mini The point cloud includes a small number of points , Their original points are interrelated . about 2048 For a point cloud ,M=64,k=3,mini The point cloud probably includes 90 A little bit .

And SOM The connection of nodes plays a role in connecting these mini The point cloud is assembled back to the original point cloud . because SOM It clearly reveals the spatial distribution of the input point cloud , Our separation and assembly process is better than the grouping strategy PointNet++ More effective .

The overall frame diagram is shown in the figure ：

4.3 Self encoder

Two parallel branches ：

5. experimental result

Data to enhance ：
The input point cloud is normalized to zero mean in a unit cube . In the training phase, the following data are used to enhance :
(a) Gaussian noise $\mathcal{N}(0,0:01)$ Add to point coordinates and face normal vectors ( If applicable );
(b) Gaussian noise $\mathcal{N}(0,0:04)$ Add to SOM node .
Point cloud 、 Surface normal vector ( If applicable ) and SOM Nodes are scaled by a factor sampled from a uniform distribution . Other additional enhancements , Such as random shift or rotation , Will not improve the results .

It can be seen that the effect was very good at that time

Robustness experiment ：

6. Conclusion and thinking

Mainly used SOM[19] To solve the point selection problem , Simulate the spatial distribution of point cloud ;

Something to explore ： Node feature extraction produces a feature matrix similar to an image , It does not change with the order of input points . As the receptive field increases , Standard can be applied ConvNets Further integrate node features . however , In our experiment , We use it 2D Convolution sum pooling Replaced the second batch of full connection layers , The classification accuracy decreased slightly . It is a promising direction to study the causes and solutions of this phenomenon .

Reference resources ：

1. https://zhuanlan.zhihu.com/p/92539221
2. https://blog.csdn.net/wydbyxr/article/details/83894383
3. https://blog.csdn.net/u011308691/article/details/19175675