# LIMP: Learning Latent Shape Representations with Metric Preservation Priors

arXiv: https://arxiv.org/abs/2003.12283 · HTML: https://mlsanity.com/paper/2003.12283/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

## Built on by (most cited first, 30 of 55)

- [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)
- [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)
- [Adversarial Parametric Pose Prior](https://mlsanity.com/paper/2112.04203/) (2021)
- [MeshMAE: Masked Autoencoders for 3D Mesh Data Analysis](https://mlsanity.com/paper/2207.10228/) (2022)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Learning disentangled representations via product manifold projection](https://mlsanity.com/paper/2103.01638/) (2021)
- [Intrinsic-Extrinsic Preserved GANs for Unsupervised 3D Pose Transfer](https://mlsanity.com/paper/2108.07520/) (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)
- [3D Shape Variational Autoencoder Latent Disentanglement via Mini-Batch Feature Swapping for Bodies and Faces](https://mlsanity.com/paper/2111.12448/) (2021)
- [Weakly-supervised 3D Pose Transfer with Keypoints](https://mlsanity.com/paper/2307.13459/) (2023)
- [AniFormer: Data-driven 3D Animation with Transformer](https://mlsanity.com/paper/2110.10533/) (2021)
- [Geometry-Contrastive Transformer for Generalized 3D Pose Transfer](https://mlsanity.com/paper/2112.07374/) (2021)
- [3inGAN: Learning a 3D Generative Model from Images of a Self-similar Scene](https://mlsanity.com/paper/2211.14902/) (2022)
- [3D Shape Sequence of Human Comparison and Classification using Current and Varifolds](https://mlsanity.com/paper/2207.12485/) (2022)
- [Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching](https://mlsanity.com/paper/2211.14604/) (2022)
- [Temporally-Coherent Surface Reconstruction via Metric-Consistent Atlases](https://mlsanity.com/paper/2104.06950/) (2021)
- [Intuitive Shape Editing in Latent Space](https://mlsanity.com/paper/2111.12488/) (2021)
- [BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes](https://mlsanity.com/paper/2211.13185/) (2022)
- [Correspondence-free online human motion retargeting](https://mlsanity.com/paper/2302.00556/) (2023)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [A structured latent space for human body motion generation](https://mlsanity.com/paper/2106.04387/) (2021)
- [Neural Human Deformation Transfer](https://mlsanity.com/paper/2109.01588/) (2021)
- [Garment Avatars: Realistic Cloth Driving using Pattern Registration](https://mlsanity.com/paper/2206.03373/) (2022)
- [Latent Spectral Regularization for Continual Learning](https://mlsanity.com/paper/2301.03345/) (2023)
- [3D Generative Model Latent Disentanglement via Local Eigenprojection](https://mlsanity.com/paper/2302.12798/) (2023)
- [Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures](https://mlsanity.com/paper/2306.15762/) (2023)

## Abstract (arXiv)

In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generative models with high fidelity, motivating the need for large training datasets. In contrast, metric preservation provides a rigorous way to control the amount of geometric distortion incurring in the construction of the latent space, leading in turn to synthetic samples of higher quality. We further demonstrate, for the first time, the adoption of differentiable intrinsic distances in the backpropagation of a geodesic loss. Our geometric priors are particularly relevant in the presence of scarce training data, where learning any meaningful latent structure can be especially challenging. The effectiveness and potential of our generative model is showcased in applications of style transfer, content generation, and shape completion.