# Image2SSM: Reimagining Statistical Shape Models from Images with Radial Basis Functions

arXiv: https://arxiv.org/abs/2305.11946 · HTML: https://mlsanity.com/paper/2305.11946/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Uncertain-DeepSSM: From Images to Probabilistic Shape Models](https://mlsanity.com/paper/2007.06516/) (2020)
- [From Images to Probabilistic Anatomical Shapes: A Deep Variational Bottleneck Approach](https://mlsanity.com/paper/2205.06862/) (2022)
- [Probabilistic 3D surface reconstruction from sparse MRI information](https://mlsanity.com/paper/2010.02041/) (2020)
- [Uncertainty Quantification in CNN-Based Surface Prediction Using Shape Priors](https://mlsanity.com/paper/1807.11272/) (2018)
- [A Comparison Study on Nonlinear Dimension Reduction Methods with Kernel Variations: Visualization, Optimization and Classification](https://mlsanity.com/paper/1910.02114/) (2019)

## Built on by (most cited first, 8 of 8)

- [Point2SSM++: Self-Supervised Learning of Anatomical Shape Models from Point Clouds](https://mlsanity.com/paper/2405.09707/) (2024)
- [ADASSM: Adversarial Data Augmentation in Statistical Shape Models From Images](https://mlsanity.com/paper/2307.03273/) (2023)
- [From Pixels to Polygons: A Survey of Deep Learning Approaches for Medical Image-to-Mesh Reconstruction](https://mlsanity.com/paper/2505.03599/) (2025)
- [SCorP: Statistics-Informed Dense Correspondence Prediction Directly from Unsegmented Medical Images](https://mlsanity.com/paper/2404.17967/) (2024)
- [Optimization-Driven Statistical Models of Anatomies using Radial Basis Function Shape Representation](https://mlsanity.com/paper/2411.15882/) (2024)
- [On the Viability of Semi-Supervised Segmentation Methods for Statistical Shape Modeling](https://mlsanity.com/paper/2407.15260/) (2024)
- [Adaptive Particle-Based Shape Modeling for Anatomical Surface Correspondence](https://mlsanity.com/paper/2507.07379/) (2025)
- [A Joint 2D-3D Statistical Shape Model for Orthopedic Reconstruction](https://mlsanity.com/paper/2609.09010/) (2026)

## Abstract (arXiv)

Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using lower-dimensional shape features, on which statistical analysis can be performed. Various methods for constructing compact shape representations have been proposed, but they involve laborious and costly steps. We propose Image2SSM, a novel deep-learning-based approach for SSM that leverages image-segmentation pairs to learn a radial-basis-function (RBF)-based representation of shapes directly from images. This RBF-based shape representation offers a rich self-supervised signal for the network to estimate a continuous, yet compact representation of the underlying surface that can adapt to complex geometries in a data-driven manner. Image2SSM can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes while requiring minimal parameter tuning and no user assistance. Once trained, Image2SSM can be used to infer low-dimensional shape representations from new unsegmented images, paving the way toward scalable approaches for SSM, especially when dealing with large cohorts. Experiments on synthetic and real datasets show the efficacy of the proposed method compared to the state-of-art correspondence-based method for SSM.