In this paper, we revisit the classical representation of 3D point clouds as linear shape models. Our key insight is to leverage deep learning to represent a collection of shapes as affine transformations of low-dimensional linear shape models. Each linear model is characterized by a shape prototype, a low-dimensional shape basis and two neural networks. The networks take as input a point cloud and predict the coordinates of a shape in the linear basis and the affine transformation which best approximate the input. Both linear models and neural networks are learned end-to-end using a single reconstruction loss. The main advantage of our approach is that, in contrast to many recent deep approaches which learn feature-based complex shape representations, our model is explicit and every operation occurs in 3D space. As a result, our linear shape models can be easily visualized and annotated, and failure cases can be visually understood. While our main goal is to introduce a compact and interpretable representation of shape collections, we show it leads to state of the art results for few-shot segmentation.



Pipeline overview. For a given input point cloud $x$, we predict for each shape model $\mathcal{R}^k$ the element that best reconstructs the input: the projection network $\mathcal{P}^k$ outputs the coordinates $a$ in the linear family, and the alignment network $\mathcal{A}^k$ predicts the parameters of an affine transformation $\mathcal{A}^k(x)$ which is applied to the selected element. The input point cloud is then assigned to the shape model that best reconstructs it, here highlighted in green.


If you find this project useful for your research, please cite:

  title={Representing Shape Collections with Alignment-Aware Linear Models}, 
  author={Romain Loiseau and Tom Monnier and Mathieu Aubry and Loïc Landrieu},
CodePaperSlidesLong videoShort video


This work was supported in part by ANR project Ready3D ANR-19-CE23-0007 and HPC resources from GENCI-IDRIS (Grant 2020-AD011012096).