PointNet

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 针对点云无序性—采用maxpooling作为对称函数。最大池化操作保留最大值，不管顺序如何变化，最大值不会改变。

针对刚体变化—对齐网络T-net

特征提取阶段采用MLP，这种结构用到的运算都是乘法和加法（对称函数），不会受到排序影响。

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Deep Learning on 3D Data

　　Volumetric CNNS/Multi-view CNNS/Spectral CNNS/Feature-based DNNS

Point cloud analysis

• Point cloud: N orderless points, each represented by a D dim coorsinate.

　　　　Properties

• • Unordered→network needs to be invariant to N! permutations of the input set
  • Interaction among points→needs to be able to capture local structures from nearby points
  • Invariance under transformations
    

• Properties of a desired neural network on point clouds　　

  • Permutation invariance 置换不变性
    • Examples: f(x₁,x₂,...x_n) = max{x₁,x₂,...x_n}

                                                 f(x₁,x₂,...x_n)=x₁+x₂+...+x_n　

• • Transformation invariance 变换不变性

 

Permutation invariance: 构