# Landmark-free Statistical Shape Modeling via Neural Flow Deformations

arXiv: https://arxiv.org/abs/2209.06861 · HTML: https://mlsanity.com/paper/2209.06861/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Rigid Motion Invariant Statistical Shape Modeling based on Discrete Fundamental Forms](https://mlsanity.com/paper/2111.06850/) (2021)

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

- [Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud](https://mlsanity.com/paper/2305.14486/) (2023)
- [Mesh2SSM: From Surface Meshes to Statistical Shape Models of Anatomy](https://mlsanity.com/paper/2305.07805/) (2023)
- [S3M: Scalable Statistical Shape Modeling through Unsupervised Correspondences](https://mlsanity.com/paper/2304.07515/) (2023)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [Implicit Neural Representations for Modeling of Abdominal Aortic Aneurysm Progression](https://mlsanity.com/paper/2303.01069/) (2023)
- [An End-to-End Deep Learning Generative Framework for Refinable Shape Matching and Generation](https://mlsanity.com/paper/2403.06317/) (2024)
- [SCorP: Statistics-Informed Dense Correspondence Prediction Directly from Unsegmented Medical Images](https://mlsanity.com/paper/2404.17967/) (2024)
- [On the Localization of Ultrasound Image Slices within Point Distribution Models](https://mlsanity.com/paper/2309.00372/) (2023)
- [Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes](https://mlsanity.com/paper/2502.07145/) (2025)
- [Automatic classification of deformable shapes](https://mlsanity.com/paper/2211.02530/) (2022)
- [Probabilistic 3D Correspondence Prediction from Sparse Unsegmented Images](https://mlsanity.com/paper/2407.01931/) (2024)

## Abstract (arXiv)

Statistical shape modeling aims at capturing shape variations of an anatomical structure that occur within a given population. Shape models are employed in many tasks, such as shape reconstruction and image segmentation, but also shape generation and classification. Existing shape priors either require dense correspondence between training examples or lack robustness and topological guarantees. We present FlowSSM, a novel shape modeling approach that learns shape variability without requiring dense correspondence between training instances. It relies on a hierarchy of continuous deformation flows, which are parametrized by a neural network. Our model outperforms state-of-the-art methods in providing an expressive and robust shape prior for distal femur and liver. We show that the emerging latent representation is discriminative by separating healthy from pathological shapes. Ultimately, we demonstrate its effectiveness on two shape reconstruction tasks from partial data. Our source code is publicly available (https://github.com/davecasp/flowssm).