# An End-to-End Deep Learning Generative Framework for Refinable Shape Matching and Generation

arXiv: https://arxiv.org/abs/2403.06317 · HTML: https://mlsanity.com/paper/2403.06317/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 10 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [SimGNN: A Neural Network Approach to Fast Graph Similarity Computation](https://mlsanity.com/paper/1808.05689/) (2018)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [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)
- [G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priors](https://mlsanity.com/paper/2212.02910/) (2022)
- [Discriminative and Generative Models for Anatomical Shape Analysison Point Clouds with Deep Neural Networks](https://mlsanity.com/paper/2010.00820/) (2020)

## Built on by (most cited first, 3 of 3)

- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes](https://mlsanity.com/paper/2502.07145/) (2025)
- [Focus, Align, and Diffuse: Time-Series-Aware Keyframe Diffusion for Cardiac Dynamic Synthesis from Sparse Observations](https://mlsanity.com/paper/2610.19050/) (2026)

## Abstract (arXiv)

Generative modelling for shapes is a prerequisite for In-Silico Clinical Trials (ISCTs), which aim to cost-effectively validate medical device interventions using synthetic anatomical shapes, often represented as 3D surface meshes. However, constructing AI models to generate shapes closely resembling the real mesh samples is challenging due to variable vertex counts, connectivities, and the lack of dense vertex-wise correspondences across the training data. Employing graph representations for meshes, we develop a novel unsupervised geometric deep-learning model to establish refinable shape correspondences in a latent space, construct a population-derived atlas and generate realistic synthetic shapes. We additionally extend our proposed base model to a joint shape generative-clustering multi-atlas framework to incorporate further variability and preserve more details in the generated shapes. Experimental results using liver and left-ventricular models demonstrate the approach's applicability to computational medicine, highlighting its suitability for ISCTs through a comparative analysis.