class XConv(in_channels: int, out_channels: int, dim: int, kernel_size: int, hidden_channels: Optional[int] = None, dilation: int = 1, bias: bool = True, num_workers: int = 1)[source]

Bases: Module

The convolutional operator on \(\mathcal{X}\)-transformed points from the “PointCNN: Convolution On X-Transformed Points” paper.

\[\mathbf{x}^{\prime}_i = \mathrm{Conv}\left(\mathbf{K}, \gamma_{\mathbf{\Theta}}(\mathbf{P}_i - \mathbf{p}_i) \times \left( h_\mathbf{\Theta}(\mathbf{P}_i - \mathbf{p}_i) \, \Vert \, \mathbf{x}_i \right) \right),\]

where \(\mathbf{K}\) and \(\mathbf{P}_i\) denote the trainable filter and neighboring point positions of \(\mathbf{x}_i\), respectively. \(\gamma_{\mathbf{\Theta}}\) and \(h_{\mathbf{\Theta}}\) describe neural networks, i.e. MLPs, where \(h_{\mathbf{\Theta}}\) individually lifts each point into a higher-dimensional space, and \(\gamma_{\mathbf{\Theta}}\) computes the \(\mathcal{X}\)- transformation matrix based on all points in a neighborhood.

  • in_channels (int) – Size of each input sample.

  • out_channels (int) – Size of each output sample.

  • dim (int) – Point cloud dimensionality.

  • kernel_size (int) – Size of the convolving kernel, i.e. number of neighbors including self-loops.

  • hidden_channels (int, optional) – Output size of \(h_{\mathbf{\Theta}}\), i.e. dimensionality of lifted points. If set to None, will be automatically set to in_channels / 4. (default: None)

  • dilation (int, optional) – The factor by which the neighborhood is extended, from which kernel_size neighbors are then uniformly sampled. Can be interpreted as the dilation rate of classical convolutional operators. (default: 1)

  • bias (bool, optional) – If set to False, the layer will not learn an additive bias. (default: True)

  • num_workers (int) – Number of workers to use for k-NN computation. Has no effect in case batch is not None, or the input lies on the GPU. (default: 1)

  • input: node features \((|\mathcal{V}|, F_{in})\), positions \((|\mathcal{V}|, D)\), batch vector \((|\mathcal{V}|)\) (optional)

  • output: node features \((|\mathcal{V}|, F_{out})\)

forward(x: Tensor, pos: Tensor, batch: Optional[Tensor] = None)[source]

Runs the forward pass of the module.


Resets all learnable parameters of the module.