mlsanityData to 7 Oct 2026

ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators

arXiv 2108.09432 ↗First posted 21 Aug 2021cs.CV cs.AI cs.GRcited by 40

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Abstract (arXiv)

This paper introduces an unsupervised loss for training parametric deformation shape generators. The key idea is to enforce the preservation of local rigidity among the generated shapes. Our approach builds on an approximation of the as-rigid-as possible (or ARAP) deformation energy. We show how to develop the unsupervised loss via a spectral decomposition of the Hessian of the ARAP energy. Our loss nicely decouples pose and shape variations through a robust norm. The loss admits simple closed-form expressions. It is easy to train and can be plugged into any standard generation models, e.g., variational auto-encoder (VAE) and auto-decoder (AD). Experimental results show that our approach outperforms existing shape generation approaches considerably on public benchmark datasets of various shape categories such as human, animal and bone.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). Builds on 46 of its 69 references that are in the map. First posted on arXiv 21 Aug 2021.

Builds on

46 of 69 references.

References · 46

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  3. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
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34 more
  1. 20163D Menagerie: Modeling the 3D shape and pose of animalscited by 310
  2. 2018Generating 3D faces using Convolutional Mesh Autoencoderscited by 267
  3. 2016Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesiscited by 219
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  5. 2016Learning Shape Abstractions by Assembling Volumetric Primitivescited by 181
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  7. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  8. 2019SDM-NET: Deep Generative Network for Structured Deformable Meshcited by 113
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  10. 2019Neural Cages for Detail-Preserving 3D Deformationscited by 105
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  12. 2019Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generationcited by 89
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  15. 2017Variational Autoencoders for Deforming 3D Mesh Modelscited by 69
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  17. 2020Unsupervised Shape and Pose Disentanglement for 3D Meshescited by 61
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 6; 2024: 12; 2025: 10; 2026: 7.

40 papers.

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  1. 2023TextDeformer: Geometry Manipulation using Text Guidancecited by 94
  2. 2022Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshescited by 28
  3. 2024Recent Trends in 3D Reconstruction of General Non-Rigid Scenescited by 28
  4. 2021Frame Averaging for Equivariant Shape Space Learningcited by 18
  5. 2022Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical frameworkcited by 18
  6. 2022SPARF: Large-Scale Learning of 3D Sparse Radiance Fields from Few Input Imagescited by 17
  7. 2025Geometry in Style: 3D Stylization via Surface Normal Deformationcited by 14
  8. 2024SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimationcited by 12
  9. 2023GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Modelscited by 11
  10. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  11. 2024DreamMesh: Jointly Manipulating and Texturing Triangle Meshes for Text-to-3D Generationcited by 9
  12. 2024A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Partscited by 8
28 more
  1. 2025Category-Agnostic Neural Object Riggingcited by 8
  2. 2022BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapescited by 7
  3. 20233D Generative Model Latent Disentanglement via Local Eigenprojectioncited by 6
  4. 2023Explorable Mesh Deformation Subspaces from Unstructured Generative Modelscited by 6
  5. 2023Basis restricted elastic shape analysis on the space of unregistered surfacescited by 5
  6. 20244DRecons: 4D Neural Implicit Deformable Objects Reconstruction from a single RGB-D Camera with Geometrical and Topological Regularizationscited by 5
  7. 2025ARAP-GS: Drag-driven As-Rigid-As-Possible 3D Gaussian Splatting Editing with Diffusion Priorcited by 5
  8. 2024Approximately Piecewise E(3) Equivariant Point Networkscited by 4
  9. 2024Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshingcited by 4
  10. 2023BLiSS: Bootstrapped Linear Shape Spacecited by 3
  11. 2024TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformationscited by 3
  12. 2024Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motionscited by 2
  13. 2025GenAnalysis: Joint Shape Analysis by Learning Man-Made Shape Generators with Deformation Regularizationscited by 2
  14. 2026NeuROK: Generative 4D Neural Object Kinematicscited by 2
  15. 2024PaNDaS: Learnable Deformation Modeling with Localized Controlcited by 1
  16. 2025ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fieldscited by 1
  17. 2025MeshMamba: State Space Models for Articulated 3D Mesh Generation and Reconstructioncited by 1
  18. 2025ERNet: Efficient Non-Rigid Registration Network for Point Sequencescited by 1
  19. 2026SGSoft: Learning Fused Semantic-Geometric Features for 3D Shape Correspondence via Template-Guided Soft Signalscited by 1
  20. 2024DualContrast: Unsupervised Disentangling of Content and Transformations with Implicit Parameterizationcited by 0
  21. 2024Neural Octahedral Field: Octahedral prior for simultaneous smoothing and sharp edge regularizationcited by 0
  22. 2025ScanMove: Motion Prediction and Transfer for Unregistered Body Meshescited by 0
  23. 2025DiLO: Disentangled Latent Optimization for Learning Shape and Deformation in Grouped Deforming 3D Objectscited by 0
  24. 2026Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshescited by 0
  25. 2026ARAPDiffusion: ARAP Regularization for Diffusion-Based Deformable Shape Space Learningcited by 0
  26. 2026GenSP: Consistent Spherical Parameterization via Learning Shape Generative Modelscited by 0
  27. 2026Deformable State Estimation for Autonomous Surgical Tissue Retraction Under Partial Observabilitycited by 0
  28. 2026Differentiable Voxelization of Surface Representationscited by 0