  We present Kernel Point Convolution (KPConv), a new design of point
convolution, i.e. that operates on point clouds without any intermediate
representation. The convolution weights of KPConv are located in Euclidean
space by kernel points, and applied to the input points close to them. Its
capacity to use any number of kernel points gives KPConv more flexibility than
fixed grid convolutions. Furthermore, these locations are continuous in space
and can be learned by the network. Therefore, KPConv can be extended to
deformable convolutions that learn to adapt kernel points to local geometry.
Thanks to a regular subsampling strategy, KPConv is also efficient and robust
to varying densities. Whether they use deformable KPConv for complex tasks, or
rigid KPconv for simpler tasks, our networks outperform state-of-the-art
classification and segmentation approaches on several datasets. We also offer
ablation studies and visualizations to provide understanding of what has been
learned by KPConv and to validate the descriptive power of deformable KPConv.
