Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Deep Non-rigid Structure-from-Motion Revisited: Canonicalization and Sequence Modeling

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Per-sequence canonicalization plus a Toeplitz context layer achieves state-of-the-art accuracy in deep non-rigid structure-from-motion.

desk verdict Per-sequence canonicalization is a genuinely simple and promising idea with strong SOTA numbers, but the central mechanism rests on an unverified one-step gradient approximation. read the letter →

arxiv 2412.07230 v1 pith:TNDQSVRN submitted 2024-12-10 cs.CV

Hui Deng , Jiawei Shi , Zhen Qin , Yiran Zhong , Yuchao Dai This is my paper · ORCID
classification cs.CV
keywords non-rigidstructurefrommotion3DreconstructionGeneralProcrusteanAnalysiscanonicalizationsequencemodelingToeplitzneuralnetworkself-expressiverepresentationlow-rankconstraint
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 motion ambiguity in non-rigid structure-from-motion is best resolved per sequence rather than per dataset, and that temporal information belongs in the sequence model's weights rather than in an additive bias. It introduces a parameter-free General Procrustean Analysis (GPA) layer that aligns each predicted 3D shape sequence to a canonical coordinate, and a gated Toeplitz context layer that encodes sequence order directly in a self-expressive coefficient matrix. On Human3.6M the combined pipeline lowers mean per-joint position error from 72.1 mm (previous best) to 66.1 mm, with consistent gains on HRNet-detected keypoints, InterHand2.6M, and 3DPW. The paper also reports that the advantage narrows on smaller or more fragmented datasets, where dataset-level canonicalization remains competitive.

What carries the argument

The central objects are a parameter-free General Procrustean Analysis (GPA) layer and a gated Toeplitz context layer. The GPA layer takes the predicted 3D sequence $\tilde{S}$ and solves $\hat{R}_i = \arg\min_{R_i} \sum_i \|R_i \tilde{S}_i - \bar{S}\|_F^2$, updating the mean shape $\bar{S}$ iteratively, so that all frames are mapped to a common canonical coordinate and only the combined motion $R_{\mathrm{motion}} = R_{\mathrm{camera}}R_{\mathrm{shape}}$ remains. The gated Toeplitz context layer computes a coefficient matrix $C = H(S')$ from the shape feature sequence and the series vector $L=[1,2,\dots,F]^T$, enforcing the self-expressive relation $S = C S'$ with temporal order encoded directly in the weights. Together with the nuclear norm $\|\hat{S}\|_*$ on the aligned sequence, these two mechanisms carry the argument.

What would settle it

Train the same pipeline with an exact, fully unrolled gradient through the GPA iteration (or with a verified bound on the one-step approximation error) and compare reconstruction error; if the exact-gradient version does not at least match the one-step version, the alignment is not the source of the reported improvement. Alternatively, on a synthetic sequence with known ground-truth $R_{\mathrm{motion}}$, measure the residual misalignment between the GPA-aligned shapes and the canonical ground truth: if the residual stays large while accuracy still improves, the gain must come from elsewhere.

Watch

Extended reading notes

Core claim

The central claim is that per-sequence canonicalization, implemented as a parameter-free GPA layer, resolves the coupled camera-object motion ambiguity of NRSfM more effectively than the dataset-level canonicalization used by earlier deep methods, and that a Toeplitz-based context layer makes temporal order a structural part of the reconstruction. Starting from per-frame shape and rotation predictions, the pipeline maps the shape sequence to a feature space, computes a coefficient matrix $C = H(S')$ from the feature sequence and the series vector $L = [1,2,\dots,F]^T$, and remaps the result to shape space; the GPA layer then aligns the sequence to a canonical coordinate by minimizing the sum of squared distances to the iteratively updated mean shape. The aligned sequence is supervised by reprojection error and the nuclear norm $\|\hat{S}\|_*$. The method reports an MPJPE of 66.1 mm on GT-H36M, 84.5 mm on HR-H36M, 8.6 mm on InterHand2.6M, and 74.4 mm on 3DPW, each better than the compared baselines.

Load-bearing premise

The load-bearing premise is that the one-step gradient approximation used to backpropagate through the GPA layer is accurate enough for the network to learn a true canonical coordinate; if that approximation is biased, the reported gains could come from the nuclear-norm loss or other components rather than from the alignment itself.

Editorial extensions

If this is right

  • If the central claim is correct, future deep NRSfM systems should align per sequence rather than over the whole dataset when sequences are long enough to support a stable Procrustes mean.
  • Encoding temporal order in the coefficient matrix of a self-expressive sequence model should be preferred over additive temporal bias, since the bias term is not directly constrained by any loss.
  • The GPA layer is parameter-free and can be discarded at inference time, so the accuracy gain does not add inference cost.
  • The reported ablations indicate that the alignment, the context layer, and the nuclear-norm loss are interdependent: removing any one hurts accuracy.
  • The method's benefit is largest on long, large-scale sequences; on smaller or fragmented datasets the paper reports that dataset-level canonicalization remains competitive.

Reading between the lines

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

  • A testable extension the authors leave implicit is whether the one-step gradient approximation of the GPA layer becomes a bottleneck on very long sequences, where many iterations are needed to converge; comparing an exactly unrolled gradient against the one-step version would isolate this.
  • The Toeplitz context layer could be doing something akin to classical trajectory-space bases, so one could measure whether its learned coefficients concentrate on low-frequency modes for smooth motions.
  • The per-sequence alignment principle could transfer to other self-supervised 3D tasks, such as articulated pose or deformable object reconstruction, whenever the input is a sequence with a stable reference frame.
  • Since the benefit shrinks for short fragments, an adaptive scheme that switches between per-sequence and per-dataset canonicalization based on sequence length might combine the strengths of both.
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

4 major / 5 minor

Summary. The paper proposes a deep NRSfM pipeline with two main contributions: a parameter-free per-sequence General Procrustean Analysis (GPA) layer for canonicalization, and a Toeplitz-based context layer for temporal sequence modeling under a self-expressive subspace constraint, together with a nuclear norm loss. The method is evaluated on Human3.6M, InterHand2.6M, 3DPW, CMU MOCAP, and short dense sequences, reporting state-of-the-art or comparable results. Ablation studies attribute the gains to the GPA layer, the context layer, and the nuclear norm loss.

Significance. If the claims are substantiated, the per-sequence GPA approach offers a simple, parameter-free alternative to dataset-level canonicalization, and the Toeplitz context layer provides a practical way to inject temporal information into deep NRSfM. The paper includes extensive comparisons with existing methods and an honest discussion of the limitations on short sequences and small datasets. The main weaknesses are the unverified gradient approximation in the GPA layer and the absence of uncertainty quantification or released code; the central idea is nonetheless a useful contribution to the community.

major comments (4)
  1. [General Procrustean Analysis Layer] The training-time behavior of the central GPA layer rests entirely on an unverified one-step gradient approximation, as stated in the paragraph following Eq. (7) and formalized in Eq. (9). The true Jacobian of the aligned output with respect to the input shapes couples every frame through the iteratively updated mean shape, and a biased approximation could allow the nuclear norm loss to be minimized without actually placing the shapes in a common canonical coordinate. This directly affects the attribution of the large ablation gap in Table 3 (Ours 66.1 vs. w/o GPA 121.1 MPJPE). The authors should provide an error bound or a comparison with exact backpropagation, and report the sensitivity of the final MPJPE to the number of GPA iterations.
  2. [Implementation Details] The loss weights alpha and beta in Eq. (14) are explicitly tuned on the evaluation benchmarks (alpha=9, beta=0.1) without any sensitivity analysis. Since the paper claims state-of-the-art results, it is important to show that the ranking is not an artifact of hyperparameter tuning. The authors should report results over a small grid of alpha and beta values, or otherwise demonstrate that the conclusions are stable across reasonable choices.
  3. [Ablation Study] The 'Ours PRN' row in Table 3 is described only as 'replace GPA Layer with PRN gradient', but PRN is a complete Procrustean regression network, not a gradient replacement, and it is unclear exactly which components were kept identical and how the PRN baseline was adapted to this pipeline. In addition, no error bars or multiple-seed results are reported anywhere in the paper, so the large gaps in Table 3 may not reflect statistically robust differences. At minimum, the main ablation and the top-line comparisons should include mean and standard deviation over several seeds.
  4. [Quantitative Result] On InterHand2.6M, MHR reports 29.1 MPJPE, an order-of-magnitude worse than C3dpo (9.8) and Seq2Seq (8.9), which suggests an inconsistent evaluation protocol across methods. Since the SOTA claim on this dataset relies on this comparison, the authors should clarify the protocol or remove the MHR entry if it is not directly comparable.
minor comments (5)
  1. [Quantitative Result] In the comparison list, 'Pre(Deng et al. 2022)' appears to be a typo for 'Seq2Seq'; please correct this reference.
  2. [General Procrustean Analysis Layer] Eq. (9) presents the gradient chain as nested inner products and the notation is difficult to parse; it should be expanded to show how the one-step truncation is actually computed.
  3. [Appendix] The appendix numbers its tables as Table 1, Table 2, and Table 3, which clashes with the main-text numbering; please use distinct numbering for supplementary tables.
  4. [General Procrustean Analysis Layer] The equation for the GPA layer (Eq. (7)) has garbled typesetting around the arg min expression; please fix the formatting.
  5. [Implementation Details] The paper does not state whether the code and trained models will be released; adding a reproducibility statement would strengthen the contribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the canonicalization and sequence-modeling claims are evaluated on held-out data against external baselines and do not reduce to fitted inputs or self-citations.

full rationale

The paper's derivation chain is self-contained. The per-sequence GPA canonicalization is a parameter-free forward optimization (Eq. 7) rooted in classical General Procrustean Analysis (Gower 1975); the paper does not define canonicalization in terms of the nuclear-norm loss that measures it. The central claim that per-sequence canonicalization beats dataset-level canonicalization is tested directly in Table 3 by replacing GPA with C3dpo's canonical loss ('Ours Canonical', 79.8 vs 66.1) and with PRN's gradient ('Ours PRN', 118.7), and against external methods (C3dpo, MHR, PRN) in Table 1. The sequence-modeling component is borrowed from the authors' own Toeplitz paper (Qin et al. 2023), and Seq2Seq is also the authors' prior work, but these citations are not load-bearing as unexamined theorems: the Toeplitz architecture is a published, code-reproduced component, and its contribution is isolated by the 'w/o Context Layer' ablation (166.7 vs 66.1). No reported result is a fitted quantity renamed as a prediction: MPJPE and Stress are computed on test sequences, and the hyperparameters (α=9, β=0.1) are fixed training weights rather than per-test fits. The one-step gradient approximation for the GPA layer is a potential correctness and sensitivity risk, but it is not circularity: an approximate backward pass does not make the ablation outcome equal to the input. The paper also openly discloses the shorter-sequence limitation in the Appendix, which is the expected behavior of an empirical claim rather than a tautology. Overall, no load-bearing step reduces, by definition or by self-citation, to its own input.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The method relies on the standard orthographic NRSfM model, a subspace self-expressiveness assumption borrowed from prior work, and an unverified one-step gradient approximation. Several loss and architecture hyperparameters are selected by hand or by fitting to validation outcomes. No new physical entities are introduced.

free parameters (5)
  • Loss weight alpha = 9
    Chosen after experiments to balance reprojection and nuclear norm terms (Implementation Details).
  • Loss weight beta = 0.1
    Chosen after experiments to weight the nuclear norm regularization.
  • Feature dimension D = 128
    Output size of the shape-to-feature linear layer g; architectural choice.
  • Sequence length F = 32
    Fixed training sequence length that affects the context layer and GPA alignment window.
  • GPA max iterations = 100
    Convergence cap for the iterative Procrustes alignment.
assumptions (3)
  • domain assumption The orthographic projection model W = Pi R S with Pi = [1 0 0; 0 1 0] applies to all evaluated sequences.
    Equation (1) defines the image formation model; it restricts the method to weak-perspective cameras and excludes perspective effects.
  • domain assumption Deforming shapes in the same sequence lie in a union of subspaces, so the self-expressive relation S = C S holds with non-trivial coefficients.
    Invoked near Eq. (10) via Zhu et al. 2014; the context layer's remixing is only meaningful if this subspace structure is present.
  • ad hoc to paper The one-step gradient approximation of the iterative GPA alignment yields a usable training signal.
    Stated in the GPA Layer section following Geng et al. 2021; no error bound or sensitivity study is provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Deep Non-rigid Structure-from-Motion Revisited: Canonicalization and Sequence Modeling." pith.science (2026). https://pith.science/paper/TNDQSVRN

@misc{pith2026241207230,
  author       = {Pith},
  title        = {Pith review of: Deep Non-rigid Structure-from-Motion Revisited: Canonicalization and Sequence Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TNDQSVRN}},
  note         = {Machine review of arXiv:2412.07230}
}
read the original abstract

Non-Rigid Structure-from-Motion (NRSfM) is a classic 3D vision problem, where a 2D sequence is taken as input to estimate the corresponding 3D sequence. Recently, the deep neural networks have greatly advanced the task of NRSfM. However, existing deep NRSfM methods still have limitations in handling the inherent sequence property and motion ambiguity associated with the NRSfM problem. In this paper, we revisit deep NRSfM from two perspectives to address the limitations of current deep NRSfM methods : (1) canonicalization and (2) sequence modeling. We propose an easy-to-implement per-sequence canonicalization method as opposed to the previous per-dataset canonicalization approaches. With this in mind, we propose a sequence modeling method that combines temporal information and subspace constraint. As a result, we have achieved a more optimal NRSfM reconstruction pipeline compared to previous efforts. The effectiveness of our method is verified by testing the sequence-to-sequence deep NRSfM pipeline with corresponding regularization modules on several commonly used datasets.

Figures

Figures reproduced from arXiv: 2412.07230 by the authors.

Figure 1
Figure 1. An overview of deep NRSfM pipeline with proposed shape sequence reconstruction and GPA layer. The whole [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The left side of the figure shows the canonicalization method in (Novotny et al. 2019), which performs random [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Fig. 3a shows the visualization result on different [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 1
Figure 1. Figure 1: We have given a detailed description of the network modules in the main text, here we give a more intuitive diagram [PITH_FULL_IMAGE:figures/full_fig_p011_1.png]
Figure 2
Figure 2. Figure 2: Visualization results of one sequence of InterHand2.6M. Different columns represent the Ground Truth and the [PITH_FULL_IMAGE:figures/full_fig_p013_2.png]
Figure 3
Figure 3. Figure 3: Visualization results of one sequence of Human3.6M. Different columns represent the Ground Truth and the recon [PITH_FULL_IMAGE:figures/full_fig_p014_3.png]
Figure 4
Figure 4. Figure 4: Visualization results of one sequence of Human3.6M. Different columns represent the Ground Truth and the recon [PITH_FULL_IMAGE:figures/full_fig_p015_4.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. Unsupervised 2D-3D lifting of non-rigid objects using local constraints

    cs.CV 2025-04 conditional novelty 7.0 of 10

    A generic MLP-Mixer trained with local low-rank subset and occlusion losses reconstructs 3D non-rigid shapes from 2D keypoints, cutting S-Up3D reconstruction error by over 70%.

Reference graph

Works this paper leans on

63 extracted references · 56 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    Agudo, A.; and Moreno-Noguer, F. 2016. Recovering pose and 3D deformable shape from multi-instance image ensembles. In In Proc. of the Asian Conf. on Computer Vision (ACCV), 291--307

    work page 2016

  4. [4]

    Akhter, I.; Sheikh, Y.; and Khan, S. 2009. In defense of orthonormality constraints for nonrigid structure from motion. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 1534--1541

    work page 2009

  5. [5]

    Akhter, I.; Sheikh, Y.; Khan, S.; and Kanade, T. 2008. Nonrigid structure from motion in trajectory space. In Adv. Neural Inform. Process. Syst. (NIPS), 41--48

    work page 2008

  6. [6]

    Bregler, C.; Hertzmann, A.; and Biermann, H. 2000. Recovering non-rigid 3D shape from image streams. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 690--696

    work page 2000

  7. [7]

    Cha, G.; Lee, M.; Cho, J.; and Oh, S. 2019. Reconstruct as far as you can: Consensus of non-rigid reconstruction from feasible regions. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 43(2): 623--637

    work page 2019

  8. [8]

    Cha, G.; Lee, M.; and Oh, S. 2019. Unsupervised 3d reconstruction networks. In Int. Conf. Comput. Vis. (ICCV), 3849--3858

    work page 2019

Show all 63 references
  1. [9]

    C.; and Huang, J.-B

    Choi, J.; Gao, C.; Messou, J. C.; and Huang, J.-B. 2019. Why can't i dance in the mall? learning to mitigate scene bias in action recognition. Adv. Neural Inform. Process. Syst. (NIPS), 32

    2019

  2. [10]

    Dai, Y.; Li, H.; and He, M. 2014. A simple prior-free method for non-rigid structure-from-motion factorization. Int. J. Comput. Vis. (IJCV), 107(2): 101--122

    2014

  3. [11]

    Deng, H.; Zhang, T.; Dai, Y.; Shi, J.; Zhong, Y.; and Li, H. 2022. Deep Non-rigid Structure-from-Motion: A Sequence-to-Sequence Translation Perspective. arXiv preprint arXiv:2204.04730

    2022 arXiv

  4. [12]

    Garg, R.; Roussos, A.; and Agapito, L. 2013 a . Dense variational reconstruction of non-rigid surfaces from monocular video. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 1272--1279

    2013

  5. [13]

    Garg, R.; Roussos, A.; and Agapito, L. 2013 b . A variational approach to video registration with subspace constraints. Int. J. Comput. Vis. (IJCV), 104: 286--314

    2013

  6. [14]

    Geng, Z.; Guo, M.-H.; Chen, H.; Li, X.; Wei, K.; and Lin, Z. 2021. Is Attention Better Than Matrix Decomposition? In Int. Conf. Learn. Represent. (ICLR)

    2021

  7. [15]

    F.; and Martinez, A

    Gotardo, P. F.; and Martinez, A. M. 2011. Computing smooth time trajectories for camera and deformable shape in structure from motion with occlusion. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 33(10): 2051--2065

    2011

  8. [16]

    Gower, J. C. 1975. Generalized procrustes analysis. Psychometrika, 40: 33--51

    1975

  9. [17]

    He, K.; Gkioxari, G.; Doll \'a r, P.; and Girshick, R. 2017. Mask r-cnn. In Int. Conf. Comput. Vis. (ICCV), 2961--2969

    2017

  10. [18]

    E.; Mohamed, A.-r.; Jaitly, N.; Senior, A.; Vanhoucke, V.; Nguyen, P.; Sainath, T

    Hinton, G.; Deng, L.; Yu, D.; Dahl, G. E.; Mohamed, A.-r.; Jaitly, N.; Senior, A.; Vanhoucke, V.; Nguyen, P.; Sainath, T. N.; et al. 2012. Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal processing magazin...

    2012

  11. [19]

    Ionescu, C.; Papava, D.; Olaru, V.; and Sminchisescu, C. 2014. Human3.6M: Large Scale Datasets and Predictive Methods for 3D Human Sensing in Natural Environments. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 36(7): 1325--1339

    2014

  12. [20]

    Kocabas, M.; Athanasiou, N.; and Black, M. J. 2020. Vibe: Video inference for human body pose and shape estimation. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 5253--5263

    2020

  13. [21]

    Kong, C.; and Lucey, S. 2021. Deep Non-Rigid Structure from Motion with Missing Data. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 43(12): 4365--4377

    2021

  14. [22]

    Krizhevsky, A.; Sutskever, I.; and Hinton, G. E. 2017. Imagenet classification with deep convolutional neural networks. Communications of the ACM, 60(6): 84--90

    2017

  15. [23]

    Kudo, Y.; Ogaki, K.; Matsui, Y.; and Odagiri, Y. 2018. Unsupervised adversarial learning of 3D human pose from 2D joint locations. In Eur. Conf. Comput. Vis. (ECCV)

    2018

  16. [24]

    Kumar, S. 2020. Non-rigid structure from motion: Prior-free factorization method revisited. In IEEE Winter Conference on Applications of Computer Vision (WACV), 51--60

    2020

  17. [25]

    Kumar, S.; Cherian, A.; Dai, Y.; and Li, H. 2018. Scalable dense non-rigid structure-from-motion: A grassmannian perspective. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 254--263

    2018

  18. [26]

    Kumar, S.; Dai, Y.; and Li, H. 2016. Multi-body non-rigid structure-from-motion. In In Proc. of the International Conf. on 3D Vision (3DV), 148--156

    2016

  19. [27]

    Kumar, S.; Dai, Y.; and Li, H. 2017. Spatio-temporal union of subspaces for multi-body non-rigid structure-from-motion. Pattern Recognition(PR), 71: 428--443

    2017

  20. [28]

    Kumar, S.; and Van Gool, L. 2022. Organic Priors in Non-rigid Structure from Motion. In Eur. Conf. Comput. Vis. (ECCV), 71--88

    2022

  21. [29]

    Lee, M.; Cho, J.; Choi, C.-H.; and Oh, S. 2013. Procrustean normal distribution for non-rigid structure from motion. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 1280--1287

    2013

  22. [30]

    Lee, M.; Choi, C.-H.; and Oh, S. 2014. A Procrustean Markov Process for Non-Rigid Structure Recovery. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR)

    2014

  23. [31]

    Liu, G.; Lin, Z.; Yan, S.; Sun, J.; Yu, Y.; and Ma, Y. 2012. Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 35(1): 171--184

    2012

  24. [32]

    Marques, M.; and Costeira, J. 2008. Optimal shape from motion estimation with missing and degenerate data. In 2008 IEEE Workshop on Motion and video Computing, 1--6

    2008

  25. [33]

    Moon, G.; Yu, S.-I.; Wen, H.; Shiratori, T.; and Lee, K. M. 2020. Interhand2. 6m: A dataset and baseline for 3d interacting hand pose estimation from a single rgb image. In Eur. Conf. Comput. Vis. (ECCV), 548--564

    2020

  26. [34]

    Novotny, D.; Ravi, N.; Graham, B.; Neverova, N.; and Vedaldi, A. 2019. C3dpo: Canonical 3d pose networks for non-rigid structure from motion. In Int. Conf. Comput. Vis. (ICCV), 7688--7697

    2019

  27. [35]

    Paladini, M.; Bartoli, A.; and Agapito, L. 2010. Sequential non-rigid structure-from-motion with the 3d-implicit low-rank shape model. In Eur. Conf. Comput. Vis. (ECCV), 15--28

    2010

  28. [36]

    Paladini, M.; Del Bue, A.; Stosic, M.; Dodig, M.; Xavier, J.; and Agapito, L. 2009. Factorization for non-rigid and articulated structure using metric projections. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2898--2905

    2009

  29. [37]

    Parashar, S.; Pizarro, D.; and Bartoli, A. 2018. Isometric Non-Rigid Shape-from-Motion with Riemannian Geometry Solved in Linear Time. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 40(10): 2442--2454

    2018

  30. [38]

    Parashar, S.; Salzmann, M.; and Fua, P. 2020. Local non-rigid structure-from-motion from diffeomorphic mappings. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2059--2067

    2020

  31. [39]

    Park, S.; Lee, M.; and Kwak, N. 2017. Procrustean regression: A flexible alignment-based framework for nonrigid structure estimation. IEEE Trans. Image Process. (TIP), 27(1): 249--264

    2017

  32. [40]

    Park, S.; Lee, M.; and Kwak, N. 2020. Procrustean regression networks: Learning 3d structure of non-rigid objects from 2d annotations. In Eur. Conf. Comput. Vis. (ECCV), 1--18

    2020

  33. [41]

    Qin, Z.; Han, X.; Sun, W.; He, B.; Li, D.; Li, D.; Dai, Y.; Kong, L.; and Zhong, Y. 2023. Toeplitz Neural Network for Sequence Modeling. In Int. Conf. Learn. Represent. (ICLR)

    2023

  34. [42]

    Shazeer, N. 2020. Glu variants improve transformer. arXiv preprint arXiv:2002.05202

    2020 arXiv

  35. [43]

    Sidhu, V.; Tretschk, E.; Golyanik, V.; Agudo, A.; and Theobalt, C. 2020. Neural dense non-rigid structure from motion with latent space constraints. In Eur. Conf. Comput. Vis. (ECCV), 204--222

    2020

  36. [44]

    Simon, T.; Valmadre, J.; Matthews, I.; and Sheikh, Y. 2017. Kronecker-Markov prior for dynamic 3D reconstruction. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 39(11): 2201--2214

    2017

  37. [45]

    Sun, K.; Xiao, B.; Liu, D.; and Wang, J. 2019. Deep High-Resolution Representation Learning for Human Pose Estimation. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 5693--5703

    2019

  38. [46]

    Tomasi, C.; and Kanade, T. 1992. Shape and motion from image streams under orthography: a factorization method. Int. J. Comput. Vis. (IJCV), 9(2): 137--154

    1992

  39. [47]

    Torresani, L.; Hertzmann, A.; and Bregler, C. 2008. Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors. IEEE Trans. Pattern Anal. Mach. Intell. (PAMI), 30(5): 878--892

    2008

  40. [48]

    Varol, A.; Salzmann, M.; Fua, P.; and Urtasun, R. 2012. A constrained latent variable model. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2248--2255

    2012

  41. [49]

    N.; Kaiser, .; and Polosukhin, I

    Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A. N.; Kaiser, .; and Polosukhin, I. 2017. Attention is all you need. In Adv. Neural Inform. Process. Syst. (NIPS), 5998--6008

    2017

  42. [50]

    von Marcard, T.; Henschel, R.; Black, M.; Rosenhahn, B.; and Pons-Moll, G. 2018. Recovering Accurate 3D Human Pose in The Wild Using IMUs and a Moving Camera. In European Conference on Computer Vision (ECCV)

    2018

  43. [51]

    Wang, C.; Lin, C.-H.; and Lucey, S. 2020. Deep nrsfm++: Towards 3d reconstruction in the wild. In In Proc. of the International Conf. on 3D Vision (3DV), 12--22

    2020

  44. [52]

    Wang, C.; and Lucey, S. 2021. PAUL: Procrustean Autoencoder for Unsupervised Lifting. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 434--443

    2021

  45. [53]

    Wu, H.; Hu, T.; Liu, Y.; Zhou, H.; Wang, J.; and Long, M. 2022. TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. arXiv preprint arXiv:2210.02186

    2022 arXiv

  46. [54]

    Xiao, J.; Chai, J.-x.; and Kanade, T. 2004. A closed-form solution to non-rigid shape and motion recovery. In Eur. Conf. Comput. Vis. (ECCV), 573--587

    2004

  47. [55]

    Xu, C.; Chen, S.; Li, M.; and Zhang, Y. 2021. Invariant teacher and equivariant student for unsupervised 3d human pose estimation. In AAAI, volume 35, 3013--3021

    2021

  48. [56]

    Xu, X.; and Dunn, E. 2021. GTT-Net: Learned Generalized Trajectory Triangulation. In Int. Conf. Comput. Vis. (ICCV), 5795--5804

    2021

  49. [57]

    T.; and Liu, C

    Yang, G.; Sun, D.; Jampani, V.; Vlasic, D.; Cole, F.; Chang, H.; Ramanan, D.; Freeman, W. T.; and Liu, C. 2021 a . Lasr: Learning articulated shape reconstruction from a monocular video. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 15980--15989

    2021

  50. [58]

    Yang, G.; Sun, D.; Jampani, V.; Vlasic, D.; Cole, F.; Liu, C.; and Ramanan, D. 2021 b . Viser: Video-specific surface embeddings for articulated 3d shape reconstruction. Adv. Neural Inform. Process. Syst. (NIPS), 34: 19326--19338

    2021

  51. [59]

    Yang, G.; Vo, M.; Neverova, N.; Ramanan, D.; Vedaldi, A.; and Joo, H. 2022. BANMo: Building Animatable 3D Neural Models From Many Casual Videos. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2863--2873

    2022

  52. [60]

    Zeng, H.; Dai, Y.; Yu, X.; Wang, X.; and Yang, Y. 2021. PR-RRN: Pairwise-Regularized Residual-Recursive Networks for Non-rigid Structure-from-Motion. In Int. Conf. Comput. Vis. (ICCV), 5600--5609

    2021

  53. [61]

    Zeng, H.; Yu, X.; Miao, J.; and Yang, Y. 2022. MHR-Net: Multiple-Hypothesis Reconstruction of Non-Rigid Shapes from 2D Views. In Eur. Conf. Comput. Vis. (ECCV), 1--17

    2022

  54. [62]

    Zhang, J.; Tu, Z.; Yang, J.; Chen, Y.; and Yuan, J. 2022. Mixste: Seq2seq mixed spatio-temporal encoder for 3d human pose estimation in video. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 13232--13242

    2022

  55. [63]

    Zhu, Y.; Huang, D.; De La Torre, F.; and Lucey, S. 2014. Complex non-rigid motion 3d reconstruction by union of subspaces. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 1542--1549

    2014

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.