mlsanityData to 7 Oct 2026

Representing Shape Collections with Alignment-Aware Linear Models

arXiv 2109.01605 ↗First posted 3 Sep 2021cs.CVcited by 7

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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.

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

Builds on

38 of 65 references.

References · 38

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26 more
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Built on by

Cited by year

Citing papers per year: 2023: 2; 2024: 3; 2025: 2.

7 papers.

  1. 2025GCE-Pose: Global Context Enhancement for Category-level Object Pose Estimationcited by 16
  2. 2023Pixel-wise Agricultural Image Time Series Classification: Comparisons and a Deformable Prototype-based Approachcited by 8
  3. 2023Learnable Earth Parser: Discovering 3D Prototypes in Aerial Scanscited by 5
  4. 2024SpaceJAM: a Lightweight and Regularization-free Method for Fast Joint Alignment of Imagescited by 5
  5. 2024MIRACLE3D: Memory-efficient Integrated Robust Approach for Continual Learning on Point Clouds via Shape Model Constructioncited by 3
  6. 2025FastJAM: a Fast Joint Alignment Model for Imagescited by 1
  7. 20243D Shape Completion with Test-Time Trainingcited by 0