Representing Shape Collections with Alignment-Aware Linear Models

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. Code and data are available at: https://romainloiseau.github.io/deep-linear-shapes