# ShapeEmbed: a self-supervised learning framework for 2D contour quantification

arXiv: https://arxiv.org/abs/2507.01009 · HTML: https://mlsanity.com/paper/2507.01009/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 65 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)
- [How Shift Equivariance Impacts Metric Learning for Instance Segmentation](https://mlsanity.com/paper/2101.05846/) (2021)
- [Invariant Shape Representation Learning For Image Classification](https://mlsanity.com/paper/2411.12201/) (2024)
- [Self-supervised Learning of Rotation-invariant 3D Point Set Features using Transformer and its Self-distillation](https://mlsanity.com/paper/2308.04725/) (2023)

## Built on by (most cited first, 4 of 4)

- [RotaTouille: Rotation Equivariant Deep Learning for Contours](https://mlsanity.com/paper/2508.16359/) (2025)
- [Training-free Spatially Grounded Geometric Shape Encoding (Technical Report)](https://mlsanity.com/paper/2604.07522/) (2026)
- [Varifold Moment Invariants for Sustainable and Explainable Contour Feature Extraction](https://mlsanity.com/paper/2606.07333/) (2026)
- [The Push-Forward Transform for Continuous and Robust Comparison of Dynamic Shapes](https://mlsanity.com/paper/2608.02306/) (2026)

## Abstract (arXiv)

The shape of objects is an important source of visual information in a wide range of applications. One of the core challenges of shape quantification is to ensure that the extracted measurements remain invariant to transformations that preserve an object's intrinsic geometry, such as changing its size, orientation, and position in the image. In this work, we introduce ShapeEmbed, a self-supervised representation learning framework designed to encode the contour of objects in 2D images, represented as a Euclidean distance matrix, into a shape descriptor that is invariant to translation, scaling, rotation, reflection, and point indexing. Our approach overcomes the limitations of traditional shape descriptors while improving upon existing state-of-the-art autoencoder-based approaches. We demonstrate that the descriptors learned by our framework outperform their competitors in shape classification tasks on natural and biological images. We envision our approach to be of particular relevance to biological imaging applications.