# Geodesic analysis in Kendall's shape space with epidemiological applications

arXiv: https://arxiv.org/abs/1906.11950 · HTML: https://mlsanity.com/paper/1906.11950/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 7 of 7)

- [Neural Networks as Paths through the Space of Representations](https://mlsanity.com/paper/2206.10999/) (2022)
- [A Kendall Shape Space Approach to 3D Shape Estimation from 2D Landmarks](https://mlsanity.com/paper/2207.12687/) (2022)
- [Sasaki Metric for Spline Models of Manifold-Valued Trajectories](https://mlsanity.com/paper/2303.17299/) (2023)
- [Predicting Shape Development: a Riemannian Method](https://mlsanity.com/paper/2212.04740/) (2022)
- [Ridge Regression on Riemannian Manifolds for Time-Series Prediction](https://mlsanity.com/paper/2411.18339/) (2024)
- [Intrinsic Gaussian Process Regression Modeling for Manifold-valued Response Variable](https://mlsanity.com/paper/2411.18989/) (2024)
- [PKSS-Align: Robust Point Cloud Registration on Pre-Kendall Shape Space](https://mlsanity.com/paper/2508.04286/) (2025)

## Abstract (arXiv)

We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.