# Predicting Shape Development: a Riemannian Method

arXiv: https://arxiv.org/abs/2212.04740 · HTML: https://mlsanity.com/paper/2212.04740/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 9 Dec 2022.

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

- [Multidimensional classification of hippocampal shape features discriminates Alzheimer's disease and mild cognitive impairment from normal aging](https://mlsanity.com/paper/1707.05961/) (2017)
- [Geodesic analysis in Kendall's shape space with epidemiological applications](https://mlsanity.com/paper/1906.11950/) (2019)
- [A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds](https://mlsanity.com/paper/2202.01180/) (2022)
- [Prediction of the progression of subcortical brain structures in Alzheimer's disease from baseline](https://mlsanity.com/paper/1711.08716/) (2017)
- [A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds](https://mlsanity.com/paper/2111.15371/) (2021)

## Built on by (most cited first, 1 of 1)

- [Predicting Brain Morphometry with MT-GNN: Mesh Evolution in Continuous Time with Graph-Based Metric Tensor Embeddings](https://mlsanity.com/paper/2608.05132/) (2026)

## Abstract (arXiv)

Predicting the future development of an anatomical shape from a single baseline observation is a challenging task. But it can be essential for clinical decision-making. Research has shown that it should be tackled in curved shape spaces, as (e.g., disease-related) shape changes frequently expose nonlinear characteristics. We thus propose a novel prediction method that encodes the whole shape in a Riemannian shape space. It then learns a simple prediction technique founded on hierarchical statistical modeling of longitudinal training data. When applied to predict the future development of the shape of the right hippocampus under Alzheimer's disease and to human body motion, it outperforms deep learning-supported variants as well as state-of-the-art.