# Basis restricted elastic shape analysis on the space of unregistered surfaces arXiv: https://arxiv.org/abs/2311.04382 ยท HTML: https://mlsanity.com/paper/2311.04382/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Builds on 35 of its 88 references that are in the map. - First posted on arXiv 7 Nov 2023. ## Builds on (most cited first, 30 of 35) - [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016) - [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021) - [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016) - [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016) - [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016) - [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018) - [Neural Body Fitting: Unifying Deep Learning and Model-Based Human Pose and Shape Estimation](https://mlsanity.com/paper/1808.05942/) (2018) - [Embodied Hands: Modeling and Capturing Hands and Bodies Together](https://mlsanity.com/paper/2201.02610/) (2022) - [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020) - [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018) - [Generating 3D People in Scenes without People](https://mlsanity.com/paper/1912.02923/) (2019) - [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019) - [Pose-NDF: Modeling Human Pose Manifolds with Neural Distance Fields](https://mlsanity.com/paper/2207.13807/) (2022) - [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021) - [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022) - [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020) - [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021) - [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021) - [FARM: Functional Automatic Registration Method for 3D Human Bodies](https://mlsanity.com/paper/1807.10517/) (2018) - [Neural Face Rigging for Animating and Retargeting Facial Meshes in the Wild](https://mlsanity.com/paper/2305.08296/) (2023) - [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013) - [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021) - [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021) - [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022) - [GLASS: Geometric Latent Augmentation for Shape Spaces](https://mlsanity.com/paper/2108.03225/) (2021) - [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021) - [Shape Analysis of Surfaces Using General Elastic Metrics](https://mlsanity.com/paper/1910.02045/) (2019) - [A numerical framework for elastic surface matching, comparison, and interpolation](https://mlsanity.com/paper/2006.11652/) (2020) - [4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data](https://mlsanity.com/paper/2101.09403/) (2021) - [A Riemannian Framework for Analysis of Human Body Surface](https://mlsanity.com/paper/2108.11449/) (2021) ## Built on by (most cited first, 5 of 5) - [Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions](https://mlsanity.com/paper/2411.03475/) (2024) - [PaNDaS: Learnable Deformation Modeling with Localized Control](https://mlsanity.com/paper/2412.02306/) (2024) - [SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data](https://mlsanity.com/paper/2506.01189/) (2025) - [ARAPDiffusion: ARAP Regularization for Diffusion-Based Deformable Shape Space Learning](https://mlsanity.com/paper/2606.06887/) (2026) - [Varifold Moment Invariants for Sustainable and Explainable Contour Feature Extraction](https://mlsanity.com/paper/2606.07333/) (2026) ## Abstract (arXiv) This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional manifold of immersed surfaces and satisfy specific invariance properties enabling the comparison of surfaces modulo shape preserving transformations such as reparametrizations. The specificity of the approach we develop is to restrict the space of allowable transformations to predefined finite dimensional bases of deformation fields. These are estimated in a data-driven way so as to emulate specific types of surface transformations observed in a training set. The use of such bases allows to simplify the representation of the corresponding shape space to a finite dimensional latent space. However, in sharp contrast with methods involving e.g. mesh autoencoders, the latent space is here equipped with a non-Euclidean Riemannian metric precisely inherited from the family of aforementioned elastic metrics. We demonstrate how this basis restricted model can be then effectively implemented to perform a variety of tasks on surface meshes which, importantly, does not assume these to be pre-registered (i.e. with given point correspondences) or to even have a consistent mesh structure. We specifically validate our approach on human body shape and pose data as well as human face scans, and show how it generally outperforms state-of-the-art methods on problems such as shape registration, interpolation, motion transfer or random pose generation.