# A Lightweight Model for 3D Point Cloud Object Detection
## 3 Method
### Lightweight 3D Sparse Convolution Layer Module  
The core part of LW-Sconv module consists of a group convolution, a transpose and reshape operation, and a depth-wise sparse convolution. The filter of the group convolution is \(1\times 1\times 1\) and the filter of the depth-wise sparse convolution is \(3\times 3\times 3\). Each convolution operation is followed by batch normalization and ReLU. Due to the 3D sparse convolution having two types (sub-manifold sparse convolution and regular sparse convolution), we describe the two types of the LW-Sconv module in Figure 1. There are three adjustable hyperparameters in the LW-Sconv module: \(g\), \(C\), and \(C^{\prime}\). \(g\) represents the number of groups in the \(1\times 1\times 1\) group convolution layer; \(C\) represents the number of filters in the group convolution layer; \(C^{\prime}\) represents the number of filters in the depth-wise sparse convolution layer. This paper sets \(C<C^{\prime}\), which limits the number of input channels of depth-wise sparse convolution. The overall goal of the lightweight model design in this paper is to change the calculation method of standard 3D sparse convolution and to identify a convolution neural network architecture with lower complexity. Therefore, this paper designs a lightweight 3D sparse convolution layer module with the following basis:  
* Using \(1\times 1\times 1\) group convolution to process the input data, not only are the parameters of the filter reduced compared with the ordinary \(3\times 3\times 3\) filter, but the \(1\times 1\times 1\) convolution after grouping is more suitable for lightweight networks with constrained complexity than the dense \(1\times 1\times 1\) convolution;
* Applying transpose and reshape operations, the feature map is concatenated from the output of different group convolutions on the previous layer. The application of transpose and reshape operations is to avoid the non-circulation of information caused by grouping, which is conducive to the subsequent extraction of global features;
* Applying \(3\times 3\times 3\) depth-wise sparse convolution, consider a standard 3D convolution, where the number of parameters in this layer is (the number of input channel) \(\times\) (the number of filter) \(\times\) (\(3\times 3\times 3\)). Using the depth-wise sparse convolution, the feature map is convolved channel-by-channel, which maintains a small number of parameters. Compared with a \(1\times 1\times 1\) filter, the receptive field becomes larger, the information read increases, and the global features obtained are better. The above lightweight sparse convolution layer module design applies the ideas of group convolution and depth-wise convolution to sparse convolution, which can be achieved by highly optimized general matrix multiplication (GEMM). Sparse convolution is similar to the standard convolution calculation process, which uses GEMM to accelerate matrix operations. Therefore, the above lightweight method is also applicable and effective in sparse convolution. The difference is that the standard convolution uses im2 col to gather and scatter, while the sparse convolution is based on the rulebook and hash table constructed in advance to construct the matrix and restore the spatial position. Due to the fact that the sparse convolution is different from the standard convolution in the way of matrix operation through GEMM, only the non-empty features in the feature map are stored when constructing the rulebook, so the feature map of size  
Figure 1: The architecture of the LW-Sconv module. (**a**) A lightweight sub-manifold sparse layer module (LW-Subsconv module). (**b**) A lightweight regular sparse layer module (LW-Regsconv module). \(H\times W\times D\times C\) represents the input size. \(H\times W\times D\times C^{\prime}\) represents the the output size. Size represents the size of the convolution kernel. Num represents the number of convolution kernels.