Pith. sign in

REVIEW 2 major objections 7 minor 1 cited by

Physics-Driven Local-Whole Elastic Deformation Modeling for Point Cloud Representation Learning

T0 review · 2 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Adding a physics-driven elastic deformation branch to a self-supervised 3D encoder improves feature quality enough to beat prior self-supervised methods on real-world scans.

desk verdict The ScanObjectNN numbers are real-world gains worth taking seriously, but the physics loss in Eq. (10) is a constant as written—most of the 'physics-driven' story needs a fix or a rewrite. read the letter →

arxiv 2505.13812 v3 pith:TJF7WTKQ submitted 2025-05-20 cs.CV

Zhongyu Chen , Rong Zhao , Xie Han , Xindong Guo , Song Wang , Zherui Qiao This is my paper · ORCID
classification cs.CV
keywords pointcloudrepresentationlearningself-supervisedphysics-informedlosselasticdeformationfiniteelementmethodimplicitfieldtetrahedralmesh3Dobjectclassification
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that a point cloud encoder learns better 3D representations when, alongside reconstructing the shape with an implicit field, it also predicts how the object would elastically deform under an external force. The deformation branch runs on a tetrahedral mesh: the encoder shares weights with the shape branch, and two losses supervise it, one matching a finite-element displacement field and one penalizing violation of the force-equilibrium equation. If correct, this means the physical propagation of local stress to global deformation is a useful self-supervised signal, not just extra geometry. The paper reports that the resulting features beat prior self-supervised methods on real-world ScanObjectNN classification and improve part and indoor segmentation.

What carries the argument

The mechanism that carries the argument is the physics information awareness module built on linear elasticity over a tetrahedral mesh. A 3D Delaunay triangulation converts each point cloud into tetrahedra; a small convolutional mesh processor feeds tetrahedron features into the same encoder used by the implicit-field branch, and the deformation decoder predicts nodal displacements $\hat{u}$. The deformation gradient is computed as $F = X' X^{-1}$, the strain as $\varepsilon = \frac{1}{2}(F+F^\top) - I$, and the stress by Hooke's law $\sigma = \lambda\,\mathrm{tr}(\varepsilon)I + 2\mu\varepsilon$. The data-fidelity loss $L_{df}$ matches $\hat{u}$ to the FEM ground truth, while the physics-informed loss $L_{pi}$ averages $\|\nabla\cdot\sigma + f\|^2$ over tetrahedra to enforce force equilibrium. The shared encoder is the point where local deformation knowledge is woven into the global shape representation.

What would settle it

Evaluate $L_{pi}$ on a single tetrahedron under a rigid translation (zero strain) and under a shear deformation; if both give the same value, the divergence term contributes nothing and the loss cannot be enforcing force balance. A direct numerical check comparing the gradient of $L_{pi}$ on a tetrahedron with a face-based traction residual would settle whether the force-equilibrium loss is genuinely active.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that explicitly modeling the relationship between local elastic responses and the whole shape, through force propagation, produces more discriminative and more transferable point cloud features than data-driven reconstruction or contrastive pretraining alone. Concretely, a shared encoder (PointNet or DGCNN) feeds both an implicit-field decoder, which predicts unsigned distance to the surface, and a physics decoder that outputs a displacement field on a Delaunay tetrahedral mesh. The physics decoder is trained with a data-fidelity loss against ground-truth finite-element displacements and a physics-informed loss enforcing $\nabla\cdot\sigma+f=0$. Evaluated with linear SVM, the pretrained encoder gives 90.3% and 92.2% on ModelNet40 and 79.5% and 86.4% on ScanObjectNN for the two backbones; fine-tuning reaches 88.0% on ScanObjectNN with DGCNN, and segmentation reaches 86.0 mean IoU on ShapeNetPart and 59.0 on S3DIS. The paper takes these results as evidence that the physics-driven branch captures local-to-whole structural coupling and improves generalization and interpretability.

Load-bearing premise

The load-bearing premise is that the force-balance loss can sense differences in deformation through the divergence of stress; in a constant-strain tetrahedron that divergence is zero, so the loss may not constrain the network at all unless a discrete traction term is added.

Editorial extensions

If this is right

  • Pretrained features transfer to linear classification: the ScanObjectNN gains over the supervised baselines are 6.2 points (PointNet) and 3.6 points (DGCNN), showing the physical pretraining helps most on real, noisy scans rather than synthetic ones.
  • Fine-tuning the pretrained encoder pushes ScanObjectNN accuracy to 88.0% with DGCNN, 3.9 points above the best comparison method the paper reports, so the representation is a strong initialization for downstream recognition.
  • The same encoder transfers to dense prediction: 86.0 mean IoU on ShapeNetPart and 59.0 on S3DIS with DGCNN, which the paper presents as competitive on both synthetic and indoor real-world segmentation.
  • Ablations show the combined implicit-plus-physics pretraining (PIA+IFL) beats either module alone, and swapping point coordinates for tetrahedral mesh input improves accuracy, so the structured discretization is load-bearing for the physics branch.
  • Saliency visualizations suggest the physics constraint moves the network's attention from scattered local details toward load-bearing regions and load-transfer paths, which is the interpretability gain the method is designed to deliver.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not run a control that replaces the FEM displacement target with a random smooth displacement field; if such a control performed equally well, the gains would come from extra geometric supervision rather than from physics specifically, a distinction the current experiments do not resolve.
  • The force-propagation story predicts that per-category gains should be largest for shapes with slender load-bearing parts (handles, arms, supports) and smallest for blob-like objects; a per-category breakdown on ShapeNetPart could test that prediction directly.
  • Because the physics branch depends on the quality of the Delaunay tetrahedralization, one testable extension is to vary mesh coarseness and measure whether downstream accuracy tracks element quality; the paper defers mesh-quality analysis to the supplementary material.
  • If the equilibrium loss is replaced by a face-based traction residual on the tetrahedron boundaries, the physics constraint would be well-defined even for constant-strain elements; that variant is a natural next step the paper does not explore.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. The manuscript proposes a self-supervised point cloud representation learning framework that couples an implicit-field reconstruction branch with a physics-aware elastic deformation branch. The point cloud is tetrahedralized by Delaunay triangulation, a mesh processor encodes tetrahedron features, and a shared encoder produces a latent code used by two decoders: one predicts unsigned distances to the surface, and the other predicts nodal displacements under linear elasticity. Training minimizes an implicit loss, a data-fidelity loss against FEM-computed displacements, and a physics-informed equilibrium loss. The pretrained encoder is transferred to linear classification, fine-tuning, and segmentation on ModelNet40, ScanObjectNN, ShapeNetPart, and S3DIS, where the authors report consistent gains over several self-supervised baselines, especially on the real-world ScanObjectNN dataset.

Significance. If confirmed, the empirical results are a meaningful contribution: reported ScanObjectNN linear classification accuracies of 79.5% and 86.4% with PointNet and DGCNN backbones, and a fine-tuned DGCNN accuracy of 88.0%, are competitive with or better than published self-supervised methods. The paper also provides ablation studies and visualizations linking deformation patterns to saliency. However, the formalization of the physics constraint is impaired by a degenerate loss term: as written, the physics-informed loss cannot provide a learning signal, so the causal attribution of the gains to 'physics' is not established. The strengths are the breadth of the evaluation and the clear motivation for combining geometric and deformation-based auxiliary tasks; the weakness is the missing or erroneous technical core of the physics loss. Because the issue is localized to Section III.C and is fixable, a major revision is appropriate rather than outright rejection.

major comments (2)
  1. [Section III.C, Eq. (10)] The physics-informed loss is degenerate as written. Under the paper's own reconstruction, the deformation gradient in Eq. (7), the strain in Eq. (8), and the stress in Eq. (9) are element-wise constant for linear tetrahedra, so the strong-form divergence in Eq. (6) is identically zero inside every tetrahedron. Eq. (10) therefore reduces to a constant penalty on the supplied force field f_il and has zero gradient with respect to the predicted displacement. This term cannot explain the ablation gains attributed to L_pi in Table V. Please replace Eq. (10) by a well-posed discrete equilibrium residual, for example the assembled nodal force imbalance sum_e B_e^T sigma_e V_e - f_ext, or a face-based traction-jump residual, and state explicitly which residual was used in training. If no such residual was used, the claims about enforcing equilibrium should be removed and the ablations re-run.
  2. [Section III.C, Eqs. (5)-(10)] The causal claim that the physics loss drives the observed improvements is not established. The ground-truth displacement u in Eq. (5) is generated by the same FEM simulation that defines the loading, and the force field f_il in Eq. (10) is prescribed by the deformation parameters tau; thus the physics branch fits simulator outputs rather than being constrained by an independent physical law. This is a legitimate multi-task self-supervision setup, but the paper should re-frame the contribution accordingly. In addition, a control experiment using a non-physical deformation target (e.g., random or smooth synthetic displacement fields) under otherwise identical multi-task training is needed to show that any benefit comes from physical modeling rather than from the auxiliary deformation regression task itself.
minor comments (7)
  1. [Table V] The checkmark alignment in Table V is ambiguous: the row described in the text as 'point cloud only' appears to include the data-fidelity loss Ldf, and the rows for tests 1, 2, and 4 are not cleanly distinguished. Please reformat the table with explicit per-row entries and define each configuration.
  2. [Section III.B, Eq. (1)] The objective in Eq. (1) is malformed; it should be written as a loss, e.g., L(theta, eta) = ..., with a proper argument, and Eq. (2) should be checked because the predicted quantity is already an unsigned distance.
  3. [Section III.A] The implicit decoder is described as predicting 'occupancy' in Section III.A, but Section III.B defines it as predicting an unsigned distance field; please align the terminology.
  4. [Section III.C] The text says 'M denotes the number of tetrahedral meshes contained in the point cloud'; this should be 'the number of tetrahedra'. The mesh filter threshold for removing large tetrahedra is also not specified in the main text.
  5. [Abstract and Section IV] The claim that the method 'outperforms existing approaches' is too broad: on ModelNet40 linear classification, CCPoint reports 92.4 with DGCNN versus 92.2 for Ours, and on ShapeNetPart, MCIB reports 86.2 versus 86.0 for Ours. Please qualify the statement.
  6. [Section IV.B] The phrases 'improvements of 2.7% and 0.2%' do not name the comparison baselines; please specify, e.g., 79.5% versus 76.8% for CrossNet with PointNet and 86.4% versus 86.2% for CCPoint with DGCNN.
  7. [Section IV.C] There is a duplicated word in 'ShapeNetPart dataset dataset', and the repeated 'GSPCon [11]' row in Table III should be removed.

Circularity Check

1 steps flagged · score 6.0 of 10

The physics-informed loss in Eq. (10) reduces by construction to a constant penalty on the supplied force field, so the claimed physical constraint is not an independent learning signal; the downstream benchmarks still provide external evidence.

  1. other [Section III.C, Eqs. (7)-(10)]
    "Finally, we define the physics-informed loss by averaging the l2 norm of the equilibrium residual over all tetrahedra: Lpi = ... ||∇·σ_il + f_il||^2, where ∇·σ_il represents the stress tensor divergence, which describes the force equilibrium within the mesh. f_il denotes the ground-truth external force at the l-th tetrahedron of the i-th sample."

    Because F = X'·X^{-1} (Eq. 7), ε = 1/2(F+F^T)-I (Eq. 8), and σ = λTr(ε)I + 2με (Eq. 9) are evaluated per tetrahedron from the four vertex displacements, each of these tensors is constant inside every tetrahedron. The strong-form divergence ∇·σ is therefore identically zero in each element. Substituting into Eq. (10) gives L_pi = (1/|D|M) Σ_i Σ_l ||f_il||^2, independent of the network-predicted displacement û and with zero gradient with respect to the encoder/decoder weights. The claimed physics constraint is thus equivalent, as written, to a penalty on the same FEM-supplied force field that generated the target displacement; it cannot guide the network or explain the Table V ablation gain attributed to L_pi.

full rationale

The central empirical claim is evaluated on held-out external benchmarks (ModelNet40, ScanObjectNN, ShapeNetPart, S3DIS) against published methods, so the reported improvements are not circular in the usual self-citation or fitted-label sense. However, the paper's own Eq. (10) defines the physics-informed loss as a strong-form residual ∇·σ + f, and under the paper's per-tetrahedron reconstruction the stress is element-wise constant, making ∇·σ = 0. Consequently, L_pi reduces to a constant multiple of ||f||^2 and provides no gradient to the predicted displacement field. The claimed learning signal from the physical equilibrium equation is therefore vacuous as written; if the implementation instead uses a weak-form or assembled nodal residual, that is a different loss and would need to be stated explicitly. This is a construction-level degeneracy of one 'prediction' (the physics constraint) rather than a self-citation chain, so the paper is partially circular in its physics mechanism but not in its overall evaluation.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim relies on hand-selected physical simulation parameters and an unverified discrete equilibrium computation, all deferred to a missing supplementary. The method therefore reduces the physics branch to a fitted surrogate of FEM output rather than an independently verified physical constraint.

free parameters (5)
  • Loss weights a and b = not reported
    Weights in Eq (11) balancing implicit, data-fidelity, and physics losses; deferred to a hyperparameter study in a missing supplementary.
  • Material properties in tau (E, nu or lambda, mu) = not reported
    Young's modulus and Poisson's ratio define the linear-elastic constitutive law in Eq (9); values are not given in the main text.
  • External loading f and boundary conditions Gamma_D = not reported
    Body force magnitude and direction, and fixed regions, determine the FEM displacement labels; configuration is deferred to supplementary.
  • Tetrahedral mesh filter threshold = not reported
    Larger tetrahedra are removed to obtain the final volume mesh (Figure 3); the threshold is not specified.
  • Adaptive scaling of tau = not reported
    Scaling based on mesh size and initial deformation magnitude is mentioned but not defined.
assumptions (4)
  • domain assumption Linear elasticity with small deformations is a valid model for point cloud shape deformation.
    Invoked in Eqs (4)-(9) to define displacement, strain, stress, and equilibrium; no justification is given for its applicability to arbitrary object categories.
  • domain assumption 3D Delaunay tetrahedralization of surface point clouds plus volume filtering yields a valid volumetric domain for FEM.
    Section III.C and Figure 3; the process is heuristic and may fail for concave or hollow shapes.
  • ad hoc to paper The equilibrium residual can be evaluated per tetrahedron as in Eq (10).
    For piecewise-linear displacement, stress is constant per tetrahedron, so its divergence is zero; the paper does not specify a discrete divergence or weak form.
  • ad hoc to paper A single encoder can process both raw point clouds and mesh-processed tetrahedral features.
    Section III.A states the mesh processor T outputs features compatible with Phi_theta, but no evidence is given that the shared backbone encodes both modalities effectively.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Physics-Driven Local-Whole Elastic Deformation Modeling for Point Cloud Representation Learning." pith.science (2026). https://pith.science/paper/TJF7WTKQ

@misc{pith2026250513812,
  author       = {Pith},
  title        = {Pith review of: Physics-Driven Local-Whole Elastic Deformation Modeling for Point Cloud Representation Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TJF7WTKQ}},
  note         = {Machine review of arXiv:2505.13812}
}
read the original abstract

Existing point cloud representation learning methods primarily rely on data-driven strategies to extract geometric information from large amounts of scattered data. However, most methods focus solely on the spatial distribution features of point clouds while overlooking the relationship between local information and the whole structure, which limits the accuracy of point cloud representation. Local information reflect the fine-grained variations of an object, while the whole structure is determined by the interaction and combination of these local features, collectively defining the object's shape. In real-world, objects undergo deformation under external forces, and this deformation gradually affects the whole structure through the propagation of forces from local regions, thereby altering the object's geometric features. Therefore, appropriately introducing a physics-driven mechanism to capture the topological relationships between local parts and the whole object can effectively mitigate for the limitations of data-driven point cloud methods in structural modeling, and enhance the generalization and interpretability of point cloud representations for downstream tasks such as understanding and recognition. Inspired by this, we incorporate a physics-driven mechanism into the data-driven method to learn fine-grained features in point clouds and model the structural relationship between local regions and the whole shape. Specifically, we design a dual-task encoder-decoder framework that combines the geometric modeling capability of data-driven implicit fields with physics-driven elastic deformation. Through the integration of physics-based loss functions, the framework is guided to predict localized deformation and explicitly capture the correspondence between local structural changes and whole shape variations.

Figures

Figures reproduced from arXiv: 2505.13812 by the authors.

Figure 1
Figure 1. (a) Intra-class deformation and force distribution under an external [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The overall architecture of the proposed method is illustrated. It consists of two modules: the implicit feature learning (IFL) module, which represents [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The point cloud is first converted into a coarse mesh form through [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Feature-space visualization (t-SNE) of learned point-cloud embeddings [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Semantic segmentation results on S3DIS (DGCNN as backbone). Different colors indicate different objects. From left to right are the top view of the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Visualisation of part segmentation results based on DGCNN backbone. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Visualization of deformation and saliency feature. From top to bottom: (1) original shapes; (2) predicted elastic deformations under the same downward [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Advances in 4D Representation: Geometry, Motion, and Interaction

    cs.CV 2025-10 conditional novelty 4.0 of 10

    A representation-centric survey of 4D generation and reconstruction, organized by geometry, motion, and interaction, with qualitative trade-off comparisons across seven representation families.

Reference graph

Works this paper leans on

66 extracted references · 50 canonical work pages · cited by 1 Pith paper

  1. [1]

    Pedestrian 3d shape understanding for person re-identification via multi-view learning,

    Z. Yu, L. Li, J. Xie, C. Wang, W. Li, and X. Ning, “Pedestrian 3d shape understanding for person re-identification via multi-view learning,”IEEE Transactions on Circuits and Systems for Video Technology, 2024

    work page 2024

  2. [2]

    Robustness-aware 3d object detection in autonomous driving: A review and outlook,

    Z. Song, L. Liu, F. Jia, Y . Luo, C. Jia, G. Zhang, L. Yang, and L. Wang, “Robustness-aware 3d object detection in autonomous driving: A review and outlook,”IEEE Transactions on Intelligent Transportation Systems, 2024

    work page 2024

  3. [3]

    Segpoint: Segment any point cloud via large language model,

    S. He, H. Ding, X. Jiang, and B. Wen, “Segpoint: Segment any point cloud via large language model,” inEuropean Conference on Computer Vision. Springer, 2025, pp. 349–367

    work page 2025

  4. [4]

    Banana: Banach fixed-point network for pointcloud segmentation with inter- part equivariance,

    C. Deng, J. Lei, W. B. Shen, K. Daniilidis, and L. J. Guibas, “Banana: Banach fixed-point network for pointcloud segmentation with inter- part equivariance,”Advances in Neural Information Processing Systems, vol. 36, 2024

    work page 2024

  5. [5]

    Pointnet: Deep learning on point sets for 3d classification and segmentation,

    C. R. Qi, H. Su, K. Mo, and L. J. Guibas, “Pointnet: Deep learning on point sets for 3d classification and segmentation,” inProceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp. 652–660

    2017

  6. [6]

    Pointnet++: Deep hierarchical feature learning on point sets in a metric space,

    C. R. Qi, L. Yi, H. Su, and L. J. Guibas, “Pointnet++: Deep hierarchical feature learning on point sets in a metric space,”Advances in neural information processing systems, vol. 30, 2017

    2017

  7. [7]

    Dynamic graph cnn for learning on point clouds,

    Y . Wang, Y . Sun, Z. Liu, S. E. Sarma, M. M. Bronstein, and J. M. Solomon, “Dynamic graph cnn for learning on point clouds,”ACM Transactions on Graphics (tog), vol. 38, no. 5, pp. 1–12, 2019

    2019

  8. [8]

    Point-dae: Denoising au- toencoders for self-supervised point cloud learning,

    Y . Zhang, J. Lin, R. Li, K. Jia, and L. Zhang, “Point-dae: Denoising au- toencoders for self-supervised point cloud learning,”IEEE Transactions on Neural Networks and Learning Systems, 2025

    work page 2025

Show all 66 references
  1. [9]

    Masked surfel prediction for self-supervised point cloud learning,

    Y . Zhang, J. Lin, C. He, Y . Chen, K. Jia, and L. Zhang, “Masked surfel prediction for self-supervised point cloud learning,”arXiv preprint arXiv:2207.03111, 2022

    2022 arXiv

  2. [10]

    Patchmixing masked autoencoders for 3d point cloud self-supervised learning,

    C. Lin, W. Xu, J. Zhu, Y . Nie, R. Cai, and X. Xu, “Patchmixing masked autoencoders for 3d point cloud self-supervised learning,”IEEE Transactions on Circuits and Systems for Video Technology, 2024

    2024

  3. [11]

    Graph spectral perturbation for 3d point cloud contrastive learning,

    Y . Han, J. Chen, J. Qian, and J. Xie, “Graph spectral perturbation for 3d point cloud contrastive learning,” inProceedings of the 31st ACM International Conference on Multimedia, 2023, pp. 5389–5398

    2023

  4. [12]

    Autoencoder for words,

    C.-Y . Liou, W.-C. Cheng, J.-W. Liou, and D.-R. Liou, “Autoencoder for words,”Neurocomputing, vol. 139, pp. 84–96, 2014

    2014

  5. [13]

    Generative adversarial networks: An overview,

    A. Creswell, T. White, V . Dumoulin, K. Arulkumaran, B. Sengupta, and A. A. Bharath, “Generative adversarial networks: An overview,”IEEE signal processing magazine, vol. 35, no. 1, pp. 53–65, 2018

    2018

  6. [14]

    Point- contrast: Unsupervised pre-training for 3d point cloud understanding,

    S. Xie, J. Gu, D. Guo, C. R. Qi, L. Guibas, and O. Litany, “Point- contrast: Unsupervised pre-training for 3d point cloud understanding,” inComputer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part III 16. Springer, 2020, pp. 574–591

    2020

  7. [15]

    Spatio-temporal self- supervised representation learning for 3d point clouds,

    S. Huang, Y . Xie, S.-C. Zhu, and Y . Zhu, “Spatio-temporal self- supervised representation learning for 3d point clouds,” inProceedings of the IEEE/CVF International Conference on Computer Vision, 2021, pp. 6535–6545

    2021

  8. [16]

    Self-supervised intra-modal and cross-modal contrastive learn- ing for point cloud understanding,

    Y . Wu, J. Liu, M. Gong, P. Gong, X. Fan, A. K. Qin, Q. Miao, and W. Ma, “Self-supervised intra-modal and cross-modal contrastive learn- ing for point cloud understanding,”IEEE Transactions on Multimedia, vol. 26, pp. 1626–1638, 2023

    2023

  9. [17]

    Pointsmile: Point self-supervised learning via curriculum mutual information,

    X. Li, M. Wei, and S. Chen, “Pointsmile: Point self-supervised learning via curriculum mutual information,”Science China Information Sci- ences, vol. 67, no. 11, p. 212104, 2024

    2024

  10. [18]

    Multi-angle point cloud- vae: Unsupervised feature learning for 3d point clouds from multi- ple angles by joint self-reconstruction and half-to-half prediction,

    Z. Han, X. Wang, Y .-S. Liu, and M. Zwicker, “Multi-angle point cloud- vae: Unsupervised feature learning for 3d point clouds from multi- ple angles by joint self-reconstruction and half-to-half prediction,” in 2019 IEEE/CVF International Conference on Computer Vision (ICCV). ...

    2019

  11. [19]

    Global-local bidirectional reasoning for un- supervised representation learning of 3d point clouds,

    Y . Rao, J. Lu, and J. Zhou, “Global-local bidirectional reasoning for un- supervised representation learning of 3d point clouds,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 5376–5385

    2020

  12. [20]

    Cross-modal contrast with image jigsaw for self-supervised representation learning of 3d point clouds,

    Y . Han, X. Yu, Y . Wang, C. Xu, and Q. Liu, “Cross-modal contrast with image jigsaw for self-supervised representation learning of 3d point clouds,” in2025 25th International Conference on Software Quality, Reliability and Security (QRS). IEEE, 2025, pp. 235–245

    2025

  13. [21]

    In- corporating physics into data-driven computer vision,

    A. Kadambi, C. de Melo, C.-J. Hsieh, M. Srivastava, and S. Soatto, “In- corporating physics into data-driven computer vision,”Nature Machine Intelligence, vol. 5, no. 6, pp. 572–580, 2023

    2023

  14. [22]

    Pointnext: Revisiting pointnet++ with improved training and scaling strategies,

    G. Qian, Y . Li, H. Peng, J. Mai, H. Hammoud, M. Elhoseiny, and B. Ghanem, “Pointnext: Revisiting pointnet++ with improved training and scaling strategies,”Advances in neural information processing systems, vol. 35, pp. 23 192–23 204, 2022

    2022

  15. [23]

    Surface representation for point clouds,

    H. Ran, J. Liu, and C. Wang, “Surface representation for point clouds,” inProceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 18 942–18 952

    2022

  16. [24]

    Pillarnext: Rethinking network designs for 3d object detection in lidar point clouds,

    J. Li, C. Luo, and X. Yang, “Pillarnext: Rethinking network designs for 3d object detection in lidar point clouds,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023, pp. 17 567–17 576

    2023

  17. [25]

    Implicit autoencoder for point-cloud self-supervised rep- resentation learning,

    S. Yan, Z. Yang, H. Li, C. Song, L. Guan, H. Kang, G. Hua, and Q. Huang, “Implicit autoencoder for point-cloud self-supervised rep- resentation learning,” inProceedings of the IEEE/CVF International Conference on Computer Vision, 2023, pp. 14 530–14 542

    2023

  18. [26]

    Multi-unit global-local registration for 3d bent tube based on implicit structural feature compatibility,

    L. Wang, Z. Wang, S. Zhang, J. Tan, Y . Lin, and Y . Xiang, “Multi-unit global-local registration for 3d bent tube based on implicit structural feature compatibility,”Advanced Engineering Informatics, vol. 65, JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021 11 p. 103...

    2021

  19. [27]

    Unsupervised point cloud pre-training via occlusion completion,

    H. Wang, Q. Liu, X. Yue, J. Lasenby, and M. J. Kusner, “Unsupervised point cloud pre-training via occlusion completion,” inProceedings of the IEEE/CVF international conference on computer vision, 2021, pp. 9782–9792

    2021

  20. [28]

    Progressive generation of 3d point clouds with hierarchical consistency,

    P. Li, X. Liu, J. Huang, D. Xia, J. Yang, and Z. Lu, “Progressive generation of 3d point clouds with hierarchical consistency,”Pattern Recognition, vol. 136, p. 109200, 2023. [Online]. Available: https: //www.sciencedirect.com/science/article/pii/S0031320322006793

    2023

  21. [29]

    Foldingnet: Point cloud auto-encoder via deep grid deformation,

    Y . Yang, C. Feng, Y . Shen, and D. Tian, “Foldingnet: Point cloud auto-encoder via deep grid deformation,” inProceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp. 206– 215

    2018

  22. [30]

    Self-supervised feature learning from partial point clouds via pose disentanglement,

    M.-S. Tsai, P.-Z. Chiang, Y .-H. Tsai, and W.-C. Chiu, “Self-supervised feature learning from partial point clouds via pose disentanglement,” in2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2022, pp. 1031–1038

    2022

  23. [31]

    Pointvst: Self-supervised pre-training for 3d point clouds via view-specific point-to-image translation,

    Q. Zhang and J. Hou, “Pointvst: Self-supervised pre-training for 3d point clouds via view-specific point-to-image translation,”IEEE Transactions on Visualization and Computer Graphics, 2023

    2023

  24. [32]

    Masked autoen- coders in 3d point cloud representation learning,

    J. Jiang, X. Lu, L. Zhao, R. Dazeley, and M. Wang, “Masked autoen- coders in 3d point cloud representation learning,”IEEE Transactions on Multimedia, vol. 27, pp. 820–831, 2025

    2025

  25. [33]

    Self-supervised deep learning on point clouds by reconstructing space,

    J. Sauder and B. Sievers, “Self-supervised deep learning on point clouds by reconstructing space,”Advances in Neural Information Processing Systems, vol. 32, 2019

    2019

  26. [34]

    Self-supervised few-shot learning on point clouds,

    C. Sharma and M. Kaul, “Self-supervised few-shot learning on point clouds,”Advances in Neural Information Processing Systems, vol. 33, pp. 7212–7221, 2020

    2020

  27. [35]

    A cross branch fusion-based contrastive learning framework for point cloud self- supervised learning,

    C. Wu, Q. Huang, K. Jin, J. Pfrommer, and J. Beyerer, “A cross branch fusion-based contrastive learning framework for point cloud self- supervised learning,” in2024 International Conference on 3D Vision (3DV). IEEE, 2024, pp. 528–538

    2024

  28. [36]

    Clr-gam: Contrastive point cloud learning with guided augmentation and feature mapping,

    S. Malla and Y .-T. Chen, “Clr-gam: Contrastive point cloud learning with guided augmentation and feature mapping,” 2023. [Online]. Available: https://arxiv.org/abs/2302.14306

    2023 arXiv

  29. [37]

    Self- supervised learning of point clouds via orientation estimation,

    O. Poursaeed, T. Jiang, H. Qiao, N. Xu, and V . G. Kim, “Self- supervised learning of point clouds via orientation estimation,” in2020 International Conference on 3D Vision (3DV). IEEE, 2020, pp. 1018– 1028

    2020

  30. [38]

    Tothe- point: Efficient contrastive learning of 3d point clouds via recycling,

    X. Li, J. Chen, J. Ouyang, H. Deng, S. Velipasalar, and D. Wu, “Tothe- point: Efficient contrastive learning of 3d point clouds via recycling,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023, pp. 21 781–21 790

    2023

  31. [39]

    Ccpoint: Contrasting corrupted point clouds for self-supervised representation learning,

    X. Xiao, S. Du, Z. Tian, M. Liu, and X. Zheng, “Ccpoint: Contrasting corrupted point clouds for self-supervised representation learning,”IEEE Transactions on Multimedia, pp. 1–14, 2025

    2025

  32. [40]

    Bootstrap your own latent-a new approach to self-supervised learning,

    J.-B. Grill, F. Strub, F. Altch ´e, C. Tallec, P. Richemond, E. Buchatskaya, C. Doersch, B. Avila Pires, Z. Guo, M. Gheshlaghi Azaret al., “Bootstrap your own latent-a new approach to self-supervised learning,” Advances in neural information processing systems, vol. 33, pp. 21...

    2020

  33. [41]

    Trusted 3d self-supervised representation learning with cross-modal settings,

    X. Han, H. Cheng, P. Shi, and J. Zhu, “Trusted 3d self-supervised representation learning with cross-modal settings,”Machine Vision and Applications, vol. 35, no. 4, pp. 1–14, 2024

    2024

  34. [42]

    Hyperbolic image-and- pointcloud contrastive learning for 3d classification,

    N. Hu, H. Cheng, Y . Xie, P. Shi, and J. Zhu, “Hyperbolic image-and- pointcloud contrastive learning for 3d classification,” in2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2024, pp. 4973–4979

    2024

  35. [43]

    Multi-trusted cross-modal information bottleneck for 3d self-supervised representation learning,

    H. Cheng, X. Han, P. Shi, J. Zhu, and Z. Li, “Multi-trusted cross-modal information bottleneck for 3d self-supervised representation learning,” Knowledge-Based Systems, vol. 283, p. 111217, 2024

    2024

  36. [44]

    Cosine mixup: A mixup strategy for point cloud contrastive representaion learning,

    G. Li, X. Gao, C. Liu, D. Liang, and B. W.-K. Ling, “Cosine mixup: A mixup strategy for point cloud contrastive representaion learning,”IEEE Transactions on Circuits and Systems II: Express Briefs, 2023

    2023

  37. [45]

    Pointmcd: Boosting deep point cloud encoders via multi-view cross-modal distillation for 3d shape recognition,

    Q. Zhang, J. Hou, and Y . Qian, “Pointmcd: Boosting deep point cloud encoders via multi-view cross-modal distillation for 3d shape recognition,”IEEE Transactions on Multimedia, 2023

    2023

  38. [46]

    Crosspoint: Self-supervised cross-modal contrastive learning for 3d point cloud understanding,

    M. Afham, I. Dissanayake, D. Dissanayake, A. Dharmasiri, K. Thi- lakarathna, and R. Rodrigo, “Crosspoint: Self-supervised cross-modal contrastive learning for 3d point cloud understanding,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 20...

    2022

  39. [47]

    The deep finite element method: A deep learning framework integrating the physics-informed neural networks with the finite element method,

    W. Xiong, X. Long, S. P. Bordas, and C. Jiang, “The deep finite element method: A deep learning framework integrating the physics-informed neural networks with the finite element method,”Computer Methods in Applied Mechanics and Engineering, vol. 436, p. 117681, 2025

    2025

  40. [48]

    Dhatt, E

    G. Dhatt, E. Lefranc ¸ois, and G. Touzot,Finite element method. John Wiley & Sons, 2012

    2012

  41. [49]

    Neural modes: Self- supervised learning of nonlinear modal subspaces,

    J. Wang, Y . Du, S. Coros, and B. Thomaszewski, “Neural modes: Self- supervised learning of nonlinear modal subspaces,” inProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024, pp. 23 158–23 167

    2024

  42. [50]

    Elastic structural analysis based on graph neural network without labeled data,

    L.-H. Song, C. Wang, J.-S. Fan, and H.-M. Lu, “Elastic structural analysis based on graph neural network without labeled data,”Computer- Aided Civil and Infrastructure Engineering, vol. 38, no. 10, pp. 1307– 1323, 2023

    2023

  43. [51]

    Graph neural network en- hanced finite element modelling,

    R. Gulakala, B. Markert, and M. Stoffel, “Graph neural network en- hanced finite element modelling,”PAMM, vol. 22, no. 1, p. e202200306, 2023

    2023

  44. [52]

    Neural unsigned distance fields for implicit function learning,

    J. Chibane, G. Pons-Mollet al., “Neural unsigned distance fields for implicit function learning,”Advances in Neural Information Processing Systems, vol. 33, pp. 21 638–21 652, 2020

    2020

  45. [53]

    Delaunay triangulation in 3d,

    P. Maur, “Delaunay triangulation in 3d,”Technical Report, Departmen. of Computer Science and Engineering, 2002

    2002

  46. [54]

    Fundamental solutions in 3d elastodynamics for the bem: A review,

    P. Dineva, G. Manolis, and F. Wuttke, “Fundamental solutions in 3d elastodynamics for the bem: A review,”Engineering Analysis with Boundary Elements, vol. 105, pp. 47–69, 2019

    2019

  47. [55]

    Hooke’s law,

    T. M. Atanackovic, A. Guran, T. M. Atanackovic, and A. Guran, “Hooke’s law,”Theory of elasticity for scientists and engineers, pp. 85– 111, 2000

    2000

  48. [56]

    Cpg: Con- trastive patch-graph learning for 3d point cloud,

    J. Zhou, Y . Song, C. Chiu, Y . Xiong, Y . Luo, and S. Song, “Cpg: Con- trastive patch-graph learning for 3d point cloud,”Pattern Recognition, p. 111954, 2025

    2025

  49. [57]

    A unified approach to interpreting self-supervised pre-training methods for 3d point clouds via interactions,

    Q. Li, J. Ruan, F. Wu, Y . Chen, Z. Wei, and W. Shen, “A unified approach to interpreting self-supervised pre-training methods for 3d point clouds via interactions,” inProceedings of the Computer Vision and Pattern Recognition Conference, 2025, pp. 27 315–27 324

    2025

  50. [58]

    Shapenet: An information- rich 3d model repository,

    A. X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Suet al., “Shapenet: An information- rich 3d model repository,”arXiv preprint arXiv:1512.03012, 2015

    2015 arXiv

  51. [59]

    3d shapenets: A deep representation for volumetric shapes,

    Z. Wu, S. Song, A. Khosla, F. Yu, L. Zhang, X. Tang, and J. Xiao, “3d shapenets: A deep representation for volumetric shapes,” inProceedings of the IEEE conference on computer vision and pattern recognition, 2015, pp. 1912–1920

    2015

  52. [60]

    Re- visiting point cloud classification: A new benchmark dataset and clas- sification model on real-world data,

    M. A. Uy, Q.-H. Pham, B.-S. Hua, T. Nguyen, and S.-K. Yeung, “Re- visiting point cloud classification: A new benchmark dataset and clas- sification model on real-world data,” inProceedings of the IEEE/CVF international conference on computer vision, 2019, pp. 1588–1597

    2019

  53. [61]

    A scalable active framework for region annotation in 3d shape collections,

    L. Yi, V . G. Kim, D. Ceylan, I.-C. Shen, M. Yan, H. Su, C. Lu, Q. Huang, A. Sheffer, and L. Guibas, “A scalable active framework for region annotation in 3d shape collections,”ACM Transactions on Graphics (ToG), vol. 35, no. 6, pp. 1–12, 2016

    2016

  54. [62]

    3d semantic parsing of large-scale indoor spaces,

    I. Armeni, O. Sener, A. R. Zamir, H. Jiang, I. Brilakis, M. Fischer, and S. Savarese, “3d semantic parsing of large-scale indoor spaces,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp. 1534–1543

    2016

  55. [63]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,”CoRR, vol. abs/1412.6980, 2014. [Online]. Available: https://api.semanticscholar.org/CorpusID:6628106

    2014 arXiv

  56. [64]

    Sgdr: Stochastic gradient descent with warm restarts,

    I. Loshchilov and F. Hutter, “Sgdr: Stochastic gradient descent with warm restarts,”arXiv preprint arXiv:1608.03983, 2016

    2016 arXiv

  57. [65]

    Support vector machine,

    S. Suthaharan and S. Suthaharan, “Support vector machine,”Machine learning models and algorithms for big data classification: thinking with examples for effective learning, pp. 207–235, 2016

    2016

  58. [66]

    Visualizing data using t-sne

    L. Van der Maaten and G. Hinton, “Visualizing data using t-sne.”Journal of machine learning research, vol. 9, no. 11, 2008

    2008

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.