# A Riemannian Framework for Analysis of Human Body Surface

arXiv: https://arxiv.org/abs/2108.11449 · HTML: https://mlsanity.com/paper/2108.11449/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 25 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [Unsupervised Shape and Pose Disentanglement for 3D Meshes](https://mlsanity.com/paper/2007.11341/) (2020)
- [Geometric Disentanglement for Generative Latent Shape Models](https://mlsanity.com/paper/1908.06386/) (2019)
- [Numerical Inversion of SRNF Maps for Elastic Shape Analysis of Genus-Zero Surfaces](https://mlsanity.com/paper/1610.04531/) (2016)
- [Shape Analysis of Surfaces Using General Elastic Metrics](https://mlsanity.com/paper/1910.02045/) (2019)

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

- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [3D Shape Sequence of Human Comparison and Classification using Current and Varifolds](https://mlsanity.com/paper/2207.12485/) (2022)
- [Generating Multiple 4D Expression Transitions by Learning Face Landmark Trajectories](https://mlsanity.com/paper/2208.00050/) (2022)
- [BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes](https://mlsanity.com/paper/2211.13185/) (2022)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions](https://mlsanity.com/paper/2411.03475/) (2024)
- [Geometric Generative Models based on Morphological Equivariant PDEs and GANs](https://mlsanity.com/paper/2403.14897/) (2024)
- [Verifier-Guided Synthetic Augmentation for 3D Human Shape Generation](https://mlsanity.com/paper/2610.04006/) (2026)

## Abstract (arXiv)

We propose a novel framework for comparing 3D human shapes under the change of shape and pose. This problem is challenging since 3D human shapes vary significantly across subjects and body postures. We solve this problem by using a Riemannian approach. Our core contribution is the mapping of the human body surface to the space of metrics and normals. We equip this space with a family of Riemannian metrics, called Ebin (or DeWitt) metrics. We treat a human body surface as a point in a "shape space" equipped with a family of Riemannian metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence it induces a metric on the "shape space" of surfaces. Using the alignment of human bodies with a given template, we show that this family of metrics allows us to distinguish the changes in shape and pose. The proposed framework has several advantages. First, we define a family of metrics with desired invariance properties for the comparison of human shape. Second, we present an efficient framework to compute geodesic paths between human shape given the chosen metric. Third, this framework provides some basic tools for statistical shape analysis of human body surfaces. Finally, we demonstrate the utility of the proposed framework in pose and shape retrieval of human body.