*July 2019*

tl;dr: Generalization of 2d conv to point cloud. Similar idea to PointNet and PointNet++, and Point CNN.

From Raquelâ€™s group. This paper is similar to pointNet in that it aggregates and propagates information directly on point cloud. However one of the advantage is that **the output may be different from the input**. So it could be a fancy interpolation method.

Cons: The math is not rigorous at all. Especially for Fig. 2, the dimensions in the architecture is completely wrong and misleading.

The method is used in ContFuse paper to merge features from camera and lidar. ContFuse used MLP to output results directly instead of modeling the weights to sum over features.

- Use MLP to approximate the point cloud kernel function with full continuous support domain.
- The kernel function gives the weighting given the relative location in the support domain.
- Arch for one layer (note that dimensions in Fig. 2 is completely off)
- input: Mx3 desired output coordinates, input points coordinates Nx3, input features NxF
- find KNN: MxKx3 and support features MxKxF
**MLP maps MxKx3 to get MxKxFxO (decomposed into FxO and MxKxO)**- get support point weights: MxKxFxO
- weighted sum of MxKxF and MxKxFxO
- output: MxO

- Multiple layers can be stacked together, if M=N, for segmentation tasks.

- Voxelizing 3D space is memory and computation inefficient.
- Need K-D tree to find nearest neighbors. This takes almost half of the inference time (16 FPS).

- There is no code with this paper, which makes it less useful. However it builds the foundation of Continous Fuse and Multi-task multi-sensor fusion papers.
- Read Point CNN paper to see the difference.