# Representing Shape Collections with Alignment-Aware Linear Models

arXiv: https://arxiv.org/abs/2109.01605 · HTML: https://mlsanity.com/paper/2109.01605/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 65 references that are in the map.
- First posted on arXiv 3 Sep 2021.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Large-scale Point Cloud Semantic Segmentation with Superpoint Graphs](https://mlsanity.com/paper/1711.09869/) (2017)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [3D Point Capsule Networks](https://mlsanity.com/paper/1812.10775/) (2018)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [Unsupervised Multi-Task Feature Learning on Point Clouds](https://mlsanity.com/paper/1910.08207/) (2019)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [OctSqueeze: Octree-Structured Entropy Model for LiDAR Compression](https://mlsanity.com/paper/2005.07178/) (2020)
- [Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning](https://mlsanity.com/paper/1904.07615/) (2019)

## Built on by (most cited first, 7 of 7)

- [GCE-Pose: Global Context Enhancement for Category-level Object Pose Estimation](https://mlsanity.com/paper/2502.04293/) (2025)
- [Pixel-wise Agricultural Image Time Series Classification: Comparisons and a Deformable Prototype-based Approach](https://mlsanity.com/paper/2303.12533/) (2023)
- [SpaceJAM: a Lightweight and Regularization-free Method for Fast Joint Alignment of Images](https://mlsanity.com/paper/2407.11850/) (2024)
- [Learnable Earth Parser: Discovering 3D Prototypes in Aerial Scans](https://mlsanity.com/paper/2304.09704/) (2023)
- [MIRACLE3D: Memory-efficient Integrated Robust Approach for Continual Learning on Point Clouds via Shape Model Construction](https://mlsanity.com/paper/2410.06418/) (2024)
- [FastJAM: a Fast Joint Alignment Model for Images](https://mlsanity.com/paper/2510.22842/) (2025)
- [3D Shape Completion with Test-Time Training](https://mlsanity.com/paper/2410.18668/) (2024)

## Abstract (arXiv)

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.