# 3D Shape Sequence of Human Comparison and Classification using Current and Varifolds

arXiv: https://arxiv.org/abs/2207.12485 · HTML: https://mlsanity.com/paper/2207.12485/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 25 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [Variational Autoencoders for Deforming 3D Mesh Models](https://mlsanity.com/paper/1709.04307/) (2017)
- [Unsupervised Shape and Pose Disentanglement for 3D Meshes](https://mlsanity.com/paper/2007.11341/) (2020)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [Geometric Disentanglement for Generative Latent Shape Models](https://mlsanity.com/paper/1908.06386/) (2019)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [A Novel Geometric Framework on Gram Matrix Trajectories for Human Behavior Understanding](https://mlsanity.com/paper/1807.00676/) (2018)
- [A numerical framework for elastic surface matching, comparison, and interpolation](https://mlsanity.com/paper/2006.11652/) (2020)
- [A Riemannian Framework for Analysis of Human Body Surface](https://mlsanity.com/paper/2108.11449/) (2021)
- [Projection-based Classification of Surfaces for 3D Human Mesh Sequence Retrieval](https://mlsanity.com/paper/2111.13985/) (2021)

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

- [BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes](https://mlsanity.com/paper/2211.13185/) (2022)
- [Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures](https://mlsanity.com/paper/2306.15762/) (2023)
- [Beyond Fixed Topologies: Unregistered Training and Comprehensive Evaluation Metrics for 3D Talking Heads](https://mlsanity.com/paper/2410.11041/) (2024)
- [Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions](https://mlsanity.com/paper/2411.03475/) (2024)
- [Explainable Binary Classification of Separable Shape Ensembles](https://mlsanity.com/paper/2410.12994/) (2024)
- [ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields](https://mlsanity.com/paper/2503.02606/) (2025)
- [SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data](https://mlsanity.com/paper/2506.01189/) (2025)
- [Varifold Moment Invariants for Sustainable and Explainable Contour Feature Extraction](https://mlsanity.com/paper/2606.07333/) (2026)

## Abstract (arXiv)

In this paper we address the task of the comparison and the classification of 3D shape sequences of human. The non-linear dynamics of the human motion and the changing of the surface parametrization over the time make this task very challenging. To tackle this issue, we propose to embed the 3D shape sequences in an infinite dimensional space, the space of varifolds, endowed with an inner product that comes from a given positive definite kernel. More specifically, our approach involves two steps: 1) the surfaces are represented as varifolds, this representation induces metrics equivariant to rigid motions and invariant to parametrization; 2) the sequences of 3D shapes are represented by Gram matrices derived from their infinite dimensional Hankel matrices. The problem of comparison of two 3D sequences of human is formulated as a comparison of two Gram-Hankel matrices. Extensive experiments on CVSSP3D and Dyna datasets show that our method is competitive with state-of-the-art in 3D human sequence motion retrieval. Code for the experiments is available at https://github.com/CRISTAL-3DSAM/HumanComparisonVarifolds.