# S3M: Scalable Statistical Shape Modeling through Unsupervised Correspondences

arXiv: https://arxiv.org/abs/2304.07515 · HTML: https://mlsanity.com/paper/2304.07515/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 15 Apr 2023.

## Builds on (most cited first, 24 of 24)

- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/1710.10370/) (2017)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [Disentangling Human Error from the Ground Truth in Segmentation of Medical Images](https://mlsanity.com/paper/2007.15963/) (2020)
- [Spectral Graph Convolutions for Population-based Disease Prediction](https://mlsanity.com/paper/1703.03020/) (2017)
- [InceptionGCN: Receptive Field Aware Graph Convolutional Network for Disease Prediction](https://mlsanity.com/paper/1903.04233/) (2019)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Space](https://mlsanity.com/paper/1701.00669/) (2017)
- [Tracked 3D Ultrasound and Deep Neural Network-based Thyroid Segmentation reduce Interobserver Variability in Thyroid Volumetry](https://mlsanity.com/paper/2108.10118/) (2021)
- [Vox2Cortex: Fast Explicit Reconstruction of Cortical Surfaces from 3D MRI Scans with Geometric Deep Neural Networks](https://mlsanity.com/paper/2203.09446/) (2022)
- [DeepSSM: A Blueprint for Image-to-Shape Deep Learning Models](https://mlsanity.com/paper/2110.07152/) (2021)
- [Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport](https://mlsanity.com/paper/2202.01537/) (2022)
- [Uncertain-DeepSSM: From Images to Probabilistic Shape Models](https://mlsanity.com/paper/2007.06516/) (2020)
- [Computational Anatomy for Multi-Organ Analysis in Medical Imaging: A Review](https://mlsanity.com/paper/1812.08577/) (2018)
- [From Images to Probabilistic Anatomical Shapes: A Deep Variational Bottleneck Approach](https://mlsanity.com/paper/2205.06862/) (2022)
- [Graphite: GRAPH-Induced feaTure Extraction for Point Cloud Registration](https://mlsanity.com/paper/2010.09079/) (2020)
- [Benchmarking off-the-shelf statistical shape modeling tools in clinical applications](https://mlsanity.com/paper/2009.02878/) (2020)
- [Landmark-free Statistical Shape Modeling via Neural Flow Deformations](https://mlsanity.com/paper/2209.06861/) (2022)
- [G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priors](https://mlsanity.com/paper/2212.02910/) (2022)
- [Learning Deep Features for Shape Correspondence with Domain Invariance](https://mlsanity.com/paper/2102.10493/) (2021)
- [Automatic identification of segmentation errors for radiotherapy using geometric learning](https://mlsanity.com/paper/2206.13317/) (2022)
- [Spatiotemporal Cardiac Statistical Shape Modeling: A Data-Driven Approach](https://mlsanity.com/paper/2209.02736/) (2022)

## Built on by (most cited first, 11 of 11)

- [Deformable 3D Gaussian Splatting for Animatable Human Avatars](https://mlsanity.com/paper/2312.15059/) (2023)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud](https://mlsanity.com/paper/2305.14486/) (2023)
- [UltrON: Ultrasound Occupancy Networks](https://mlsanity.com/paper/2509.08991/) (2025)
- [On the Localization of Ultrasound Image Slices within Point Distribution Models](https://mlsanity.com/paper/2309.00372/) (2023)
- [SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization](https://mlsanity.com/paper/2603.12937/) (2026)
- [Cortex-Grounded Diffusion Models for Brain Image Generation](https://mlsanity.com/paper/2601.19498/) (2026)
- [DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisited](https://mlsanity.com/paper/2604.10377/) (2026)
- [PRISM: Probabilistic Representation for Integrated Shape Modeling and Generation](https://mlsanity.com/paper/2504.04454/) (2025)
- [AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging](https://mlsanity.com/paper/2604.02290/) (2026)

## Abstract (arXiv)

Statistical shape models (SSMs) are an established way to represent the anatomy of a population with various clinically relevant applications. However, they typically require domain expertise, and labor-intensive landmark annotations to construct. We address these shortcomings by proposing an unsupervised method that leverages deep geometric features and functional correspondences to simultaneously learn local and global shape structures across population anatomies. Our pipeline significantly improves unsupervised correspondence estimation for SSMs compared to baseline methods, even on highly irregular surface topologies. We demonstrate this for two different anatomical structures: the thyroid and a multi-chamber heart dataset. Furthermore, our method is robust enough to learn from noisy neural network predictions, potentially enabling scaling SSMs to larger patient populations without manual segmentation annotation.