# Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes

arXiv: https://arxiv.org/abs/2502.07145 · HTML: https://mlsanity.com/paper/2502.07145/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 58 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [A large annotated medical image dataset for the development and evaluation of segmentation algorithms](https://mlsanity.com/paper/1902.09063/) (2019)
- [AbdomenCT-1K: Is Abdominal Organ Segmentation A Solved Problem?](https://mlsanity.com/paper/2010.14808/) (2020)
- [VerSe: A Vertebrae Labelling and Segmentation Benchmark for Multi-detector CT Images](https://mlsanity.com/paper/2001.09193/) (2020)
- [Unsupervised Learning of Intrinsic Structural Representation Points](https://mlsanity.com/paper/2003.01661/) (2020)
- [Dual Geometric Graph Network (DG2N) -- Iterative network for deformable shape alignment](https://mlsanity.com/paper/2011.14723/) (2020)
- [DeepSSM: A Deep Learning Framework for Statistical Shape Modeling from Raw Images](https://mlsanity.com/paper/1810.00111/) (2018)
- [DeepSSM: A Blueprint for Image-to-Shape Deep Learning Models](https://mlsanity.com/paper/2110.07152/) (2021)
- [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)
- [Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud](https://mlsanity.com/paper/2305.14486/) (2023)
- [Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction](https://mlsanity.com/paper/2109.04398/) (2021)
- [Mesh2SSM: From Surface Meshes to Statistical Shape Models of Anatomy](https://mlsanity.com/paper/2305.07805/) (2023)
- [Landmark-free Statistical Shape Modeling via Neural Flow Deformations](https://mlsanity.com/paper/2209.06861/) (2022)
- [dpVAEs: Fixing Sample Generation for Regularized VAEs](https://mlsanity.com/paper/1911.10506/) (2019)
- [DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting](https://mlsanity.com/paper/2407.17058/) (2024)
- [An End-to-End Deep Learning Generative Framework for Refinable Shape Matching and Generation](https://mlsanity.com/paper/2403.06317/) (2024)

## Built on by (most cited first, 2 of 2)

- [MorphoFlow: Sparse-Supervised Generative Shape Modeling with Adaptive Latent Relevance](https://mlsanity.com/paper/2604.11636/) (2026)
- [SCALP: Semi-Supervised Statistical Shape Modeling from Imperfect 3D Photogrammetry via Landmark-Anchored Spectral Warp](https://mlsanity.com/paper/2608.00187/) (2026)

## Abstract (arXiv)

Anatomy evaluation is crucial for understanding the physiological state, diagnosing abnormalities, and guiding medical interventions. Statistical shape modeling (SSM) is vital in this process. By enabling the extraction of quantitative morphological shape descriptors from MRI and CT scans, SSM provides comprehensive descriptions of anatomical variations within a population. However, the effectiveness of SSM in anatomy evaluation hinges on the quality and robustness of the shape models. While deep learning techniques show promise in addressing these challenges by learning complex nonlinear representations of shapes, existing models still have limitations and often require pre-established shape models for training. To overcome these issues, we propose Mesh2SSM++, a novel approach that learns to estimate correspondences from meshes in an unsupervised manner. This method leverages unsupervised, permutation-invariant representation learning to estimate how to deform a template point cloud into subject-specific meshes, forming a correspondence-based shape model. Additionally, our probabilistic formulation allows learning a population-specific template, reducing potential biases associated with template selection. A key feature of Mesh2SSM++ is its ability to quantify aleatoric uncertainty, which captures inherent data variability and is essential for ensuring reliable model predictions and robust decision-making in clinical tasks, especially under challenging imaging conditions. Through extensive validation across diverse anatomies, evaluation metrics, and downstream tasks, we demonstrate that Mesh2SSM++ outperforms existing methods. Its ability to operate directly on meshes, combined with computational efficiency and interpretability through its probabilistic framework, makes it an attractive alternative to traditional and deep learning-based SSM approaches.