Pith. sign in

REVIEW 4 major objections 5 minor 71 references

Gaussians on their Way: Wasserstein-Constrained 4D Gaussian Splatting with State-Space Modeling

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read A state-space filter and Wasserstein geometry make 4D Gaussian splatting more accurate on moving scenes.

desk verdict High-level idea worth exploring, but the core equations don't hold together and the reported training-time gains are unexplained. read the letter →

arxiv 2412.00333 v3 pith:RS37MENX submitted 2024-11-30 cs.CV

Junli Deng , Yihao Luo This is my paper · ORCID
classification cs.CV
keywords 4DGaussiansplattingdynamicscenerenderingWassersteindistancestate-spacemodelingKalmanfilterdeformationfieldtemporalconsistencynovelviewsynthesis
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 is trying to establish that dynamic-scene rendering improves when each 3D Gaussian is treated not as a bag of parameters but as a full Gaussian distribution that travels through Wasserstein space under a state-space model. It adds a state consistency filter that merges a deformation network's observation with a constant-velocity prediction, a Wasserstein-distance regularization that penalizes abrupt frame-to-frame changes, and Wasserstein logarithmic and exponential maps that replace Euclidean velocity and prediction updates. On standard synthetic and real-world dynamic benchmarks the full combination reports 34.45 and 32.79 dB PSNR, with the ablations attributing about 2 dB of the gain and 51 to 57 percent training-time savings to the Wasserstein components. A sympathetic reader would summarize the contribution as a geometric, physically motivated way to keep Gaussians consistent over time, uniting position and shape in one update.

What carries the argument

The load-bearing object is the squared 2-Wasserstein distance between two Gaussians, $W_2^2(\mathcal N_1,\mathcal N_2)=\|\mu_1-\mu_2\|^2+\mathrm{Tr}(\Sigma_1+\Sigma_2-2(\Sigma_1\Sigma_2)^{1/2})$, together with the Wasserstein logarithmic and exponential maps on the manifold of symmetric positive-definite covariance matrices. The logarithmic map computes the velocity as a tangent vector from the previous Gaussian, the exponential map predicts the next Gaussian by solving a Sylvester equation, and the Kalman-like update in Eq. (6) merges that prediction with the network observation using a gain built from the two covariances. These formulas carry the argument: the stated quality and speed gains depend on the merged covariance remaining a valid symmetric positive-definite matrix and on the Wasserstein distance being the right coupling between position and shape.

What would settle it

Take two non-commuting symmetric positive-definite matrices, compute the merged covariance by Eq. (6), and check whether it is symmetric and positive definite; if it fails on generic inputs, then the core update is not well-defined and the reported gains would need a repair step. A cleaner experiment would rerun the paper's full ablation with the merge replaced by a symmetrized, SPD-projected version and compare PSNR and training time on the same scenes.

Watch

Extended reading notes

Core claim

The central claim is that the natural state space for time-varying 3D Gaussians is the metric space of Gaussian distributions under the 2-Wasserstein distance, so dynamics should be written with exp and log maps there rather than as independent Euclidean increments of means and covariances. The paper implements this claim by using the deformation network's output as an observation, a constant-velocity prior as the prediction, and a Kalman-like gain to merge the two; the merged distribution is then rendered. It further claims that penalizing the Wasserstein distance between consecutive merged Gaussians is what suppresses flicker, because the metric couples translation and shape changes in a way that the Frobenius norm or mean-only regularization cannot. The quantitative assertion is that this package outperforms prior dynamic-scene renderers on the two benchmarks tested while cutting training time roughly in half.

Load-bearing premise

The load-bearing premise is that Eq. (6) is a valid way to merge two Gaussians: the gain $K=\Sigma^{\mathrm{Ob}}_t(\Sigma^{\mathrm{Ob}}_t+\Sigma^{\mathrm{P}}_t)^{-1}$ can make the merged covariance asymmetric or non-positive-definite when the two covariances do not commute, and the paper gives no symmetrization or SPD projection before rendering.

Editorial extensions

If this is right

  • If the paper is right, dynamic-scene renderers can obtain temporally coherent output without per-frame retraining, because the filter plus Wasserstein regularization keep adjacent Gaussians close in distribution.
  • The same Wasserstein log and exp dynamics could replace Euclidean deformation prediction in other Gaussian-splatting variants, making motion estimates more physically plausible.
  • The reported training-time reductions, from 3.5 to 1.5 hours on the synthetic benchmark and 4.5 to 2.2 hours on the real-world one, suggest that geometric regularization is a cheaper way to guide optimization than unconstrained parameter tuning.
  • Because the filter produces a cleaner motion field, the approach yields a natural speed field that can be projected to optical flow and could serve as motion supervision for other tasks.

Reading between the lines

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

  • Beyond the paper, a strict test would replace the Wasserstein log and exp maps with SPD-projected Euclidean updates while keeping the same losses; if quality is unchanged, the manifold geometry is not the active ingredient and the gains come from the smoothing losses alone.
  • The Kalman-like merge as written is not symmetric when the observation and prediction covariances do not commute, so an obvious extension is a proper Riemannian or projected filter; the paper's own experiments suggest the numerical optimizer may be implicitly repairing invalid covariances.
  • The same Wasserstein regularization idea could transfer to NeRF-style dynamic fields or voxel grids, but only in latent or distributional form, since those representations lack explicit Gaussian covariances.
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 4D Gaussian Splatting framework with three components: a State Consistency Filter that merges predicted and observed Gaussian states via a Kalman-like update, a Wasserstein distance regularization term, and Wasserstein log/exp maps for dynamic prediction. The method is evaluated on the D-NeRF and Plenoptic Video datasets, reporting state-of-the-art PSNR/SSIM/LPIPS figures (34.45 dB on D-NeRF and 32.79 dB on Plenoptic) together with training-time reductions. The central claim is that combining state-space modeling with Wasserstein geometry yields more accurate, temporally coherent, and physically plausible dynamic scene rendering.

Significance. If the proposed components were correctly defined and the empirical results were reproducible, the paper would be a useful contribution to dynamic scene rendering, since it integrates distributional geometry with 4D Gaussian Splatting and provides extensive comparisons and ablations on two benchmarks. The paper deserves credit for its broad experimental coverage, per-scene tables, and explicit attempts to ablate each component. However, the mathematical core of the method contains load-bearing errors: the State Consistency Filter is not a well-defined operation on Gaussian distributions, and the Wasserstein logarithmic map is stated inconsistently between the text and Algorithm 2. These errors mean that the reported quality gains cannot be attributed to the method as written. The per-scene analysis also contains numerical claims that do not match the reported tables. The significance of the contribution is therefore currently not established.

major comments (4)
  1. [Sec. 3.1.3, Eq. (6)] The proposed merging rule is not a well-defined operation on Gaussian distributions. The Kalman gain K = Σ_t^Ob(Σ_t^Ob + Σ_t^P)^{-1} is a 3×3 matrix, while N_t^P and N_t^Ob are tuples (μ, Σ); the expression N_t^Ob + K(N_t^P - N_t^Ob) is undefined unless a block-diagonal application to μ and Σ is specified, which is not given. If the formula is applied elementwise to the covariance, the update \(\hat \Sigma_t = \Sigma_t^{Ob} + K(\Sigma_t^P - \Sigma_t^{Ob})\) is not guaranteed to be symmetric or positive definite when Σ_t^Ob and Σ_t^P do not commute, and no symmetrization or SPD projection is provided. Because 3D Gaussian Splatting represents Σ as R S S^T R^T, an invalid \(\hat \Sigma_t\) makes rasterization undefined. In a standard Kalman filter the covariance update is not a convex combination of the prior and observation covariances; the 'no noise distribution' simplification in Sec. 3.1.3 removes the mechanism that makes the Kalman gain meaningful. The State Consistency Filter, a central claimed contribution, is therefore mathematically undefined as written.
  2. [Sec. 3.3.1, Eq. (12) and Algorithm 2] The logarithmic map formula is internally contradictory and is not used consistently. The text states \(\log_{\Sigma_t} \Sigma_{t-1} = (\Sigma_t \Sigma_{t-1})^{1/2} + (\Sigma_{t-1} \Sigma_t)^{1/2} - 2\Sigma_{t-1}\) and then identifies this with \(P + P^T - 2\Sigma_t\), where \(P = \Sigma_{t-1}^{1/2}(\Sigma_{t-1}^{1/2} \Sigma_t \Sigma_{t-1}^{1/2})^{1/2} \Sigma_t^{-1/2}\). These two expressions differ in both sign of the P terms and in the subscript of the last term. Algorithm 2 sets \(\Delta\Sigma_t = 2\Sigma_{t-1} - P - P^T\), which is neither of them. Since \(\Delta\Sigma_t\) is the input to the exponential map in Eq. (14), the Wasserstein prediction step is not well-defined. The authors should state the correct formula and ensure the algorithm matches it.
  3. [Sec. 4.3.1, Tables 3 and 4] The per-scene analysis reports numbers that do not appear in the tables. The text states that in Hell Warrior 'Def-3D-Gauss achieves the highest PSNR of 41.54, while our method follows closely with 39.06'; Table 3 lists Hell Warrior Def-3D-Gauss as 32.37 and Ours as 34.38, and Table 4 lists 38.55 and 38.77. Similarly, the text claims 'in the Lego scene, our method achieves a PSNR of 34.74, surpassing 4D-Rotor-Gauss by approximately 9.5 dB,' while Table 3 Lego Ours is 30.14 and 4D-Rotor-Gauss is 29.48, and Table 4 lists 24.74 and 24.93. The text also gives Bouncing Balls PSNR 42.79, not found in either table. The per-scene discussion is therefore not supported by the reported tables, and the experimental claims cannot be independently checked.
  4. [Sec. 3.3 and Sec. 2.2] The paper claims that 'no previous work gave explicit and differentiable algorithms of Wasserstein geometry on Gaussians and involved such powerful tools in 3D/4D Gaussian Splatting,' yet the formulas in Eqs. (12)–(15) are taken directly from reference [37] without derivation. This overstates the novelty and places the mathematical backbone on a self-citation: [37] is co-authored by a co-author of this paper. For the reader to verify the method, the formulas should either be re-derived or the dependence on [37] should be clearly scoped; moreover, the correctness of the formulas should be checked independently, especially given the inconsistency identified in Eq. (12).
minor comments (5)
  1. [Sec. 3.1.2, Eq. (4)] Equation (4) assigns v_t^P twice; the intended velocity update should be stated once. Also, the notation N_t is used for both a probability distribution and a state tuple, which makes expressions such as \(N_t^{Ob} + K(N_t^P - N_t^{Ob})\) ambiguous even if a block-diagonal structure were supplied.
  2. [Table 3 caption] The caption of Table 3 says results are 'after applying the specified metric offsets,' but no offsets are specified in the text or caption; this must be clarified before the table can be used for comparison.
  3. [Sec. 4.1 and Algorithm 3] The training schedule is under-specified: the Filter is said to be 'introduced after 6k iterations' in Sec. 4.1, while Algorithm 3 applies the filter from the first iteration; the gating rule based on \(\|\mu_{\text{pred}} - \mu_{\text{obs}}\| < 0.1\sigma\) and the >3\sigma reversion are not reflected in the algorithm listings.
  4. [References] References [65] and [67] are the same paper (4D Gaussian Splatting); this duplicate citation should be corrected.
  5. [Figure 1] In Figure 1, the label 'Diff Gaussian Rasterization' appears to be a typo for 'Differentiable Gaussian Rasterization.' Also, the per-scene tables use different background settings (white vs black) with no statement of which setting is used for the aggregate Tables 1 and 2; this should be stated for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the core claims are benchmarked against external datasets, and the self-cited Wasserstein log/exp formulas are parameter-free mathematical facts.

full rationale

The derivation chain is not circular. The State Consistency Filter (Eq. 6) is a recursive estimator that merges a deform-network observation with a dynamics prediction; it is not a fitted parameter renamed as a prediction. The SOA loss (Eq. 9) and Wasserstein regularization (Eq. 10) are training regularizers and are not reported as held-out predictions, so the fitted-input-called-prediction pattern does not apply. The Wasserstein log/exp updates (Eqs. 11-15, Algorithm 2) are imported from [37], which is co-authored by one of the present authors, but they are parameter-free mathematical statements about SPD(n) whose assumptions do not include any rendering result; under the review rules such a citation counts as independent support and does not raise the circularity score. The main quality claims in Tables 1-7 are measured against external D-NeRF and Plenoptic benchmarks with ablations, so they are empirically falsifiable rather than forced by construction. Concerns about Eq. (6) producing asymmetric or non-SPD covariances, and about the sign inconsistency between Eq. (12) and Algorithm 2, are correctness or validity issues, not circularity, and are therefore not scored here.

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

The method introduces no new physical entities; the 'State Consistency Filter' is an algorithmic component. The central claim rests on hyperparameters, the co-authored Wasserstein geometry formulas, the fixed-index correspondence, and the heuristic Kalman-like fusion.

free parameters (4)
  • lambda_SOA (state-observation alignment loss weight) = 0.1
    Hyperparameter balancing the alignment loss in Eq. (16); chosen by hand, no sensitivity analysis.
  • lambda_WR (Wasserstein regularization weight) = 0.01
    Hyperparameter in Eq. (16); hand-set, no sensitivity analysis.
  • Filter engagement thresholds = 0.1 sigma and 3 sigma
    Gaussians only pass through the state-consistency filter when predicted-observed center distance is below 0.1 sigma, and revert to standard 3DGS optimization beyond 3 sigma; these thresholds select which Gaussians receive the filter, affecting the central claim.
  • Training schedule for filter and losses = 3k, 6k, 20k iterations
    Filter introduced at 6k iterations, SOA and WR losses activated at 20k, with an initial 3k iterations for 3DGS-only optimization; hand-chosen schedule, no ablation on the schedule.
assumptions (4)
  • domain assumption Wasserstein log/exp map formulas from [37] are correct and applicable to SPD(3) covariances in 3D Gaussian splatting.
    Eqs. (12)-(15) invoke logarithmic and exponential maps on the Wasserstein manifold of Gaussians, taken from the co-authored reference [37] without derivation in this paper.
  • ad hoc to paper Kalman filter update equations can be applied to Gaussian parameters as whole elements with the same gain for mean and covariance.
    Eq. (6) applies the Kalman gain K to both the mean and covariance, which is not a standard Kalman covariance update; it is a heuristic that the paper asserts without proof.
  • domain assumption Fixed batch indexing maintains persistent correspondence between Gaussian i at time t and time t-1.
    Sec. 4.1 states 'We establish correspondences via fixed batch indexing'; this assumes no reordering or topology change of Gaussians across frames.
  • domain assumption The squared 2-Wasserstein distance between rendered Gaussian distributions is the appropriate temporal-consistency metric.
    Used in Eqs. (7)-(10) without comparative justification against other distributional metrics.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Gaussians on their Way: Wasserstein-Constrained 4D Gaussian Splatting with State-Space Modeling." pith.science (2026). https://pith.science/paper/RS37MENX

@misc{pith2026241200333,
  author       = {Pith},
  title        = {Pith review of: Gaussians on their Way: Wasserstein-Constrained 4D Gaussian Splatting with State-Space Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RS37MENX}},
  note         = {Machine review of arXiv:2412.00333}
}
read the original abstract

Dynamic scene rendering has taken a leap forward with the rise of 4D Gaussian Splatting, but there's still one elusive challenge: how to make 3D Gaussians move through time as naturally as they would in the real world, all while keeping the motion smooth and consistent. In this paper, we unveil a fresh approach that blends state-space modeling with Wasserstein geometry, paving the way for a more fluid and coherent representation of dynamic scenes. We introduce a State Consistency Filter that merges prior predictions with the current observations, enabling Gaussians to stay true to their way over time. We also employ Wasserstein distance regularization to ensure smooth, consistent updates of Gaussian parameters, reducing motion artifacts. Lastly, we leverage Wasserstein geometry to capture both translational motion and shape deformations, creating a more physically plausible model for dynamic scenes. Our approach guides Gaussians along their natural way in the Wasserstein space, achieving smoother, more realistic motion and stronger temporal coherence. Experimental results show significant improvements in rendering quality and efficiency, outperforming current state-of-the-art techniques.

Figures

Figures reproduced from arXiv: 2412.00333 by the authors.

Figure 1
Figure 1. Overview of our proposed method. Starting from a Structure-from-Motion (SFM) point cloud, we initialize canonical 3D [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Gaussian dynamics modeling in Wasserstein space. The [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Qualitative results on the synthetic dataset. Zoom in for details. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Qualitative results on the real-world dataset. Zoom in for details. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 6
Figure 6. Figure 6: Wasserstein regularization effect on temporal consis [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 5
Figure 5. Figure 5: Optical Flow Visualization. Our method naturally de [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 7
Figure 7. Figure 7: Effect of Wasserstein geometry modeling. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 58 canonical work pages

  1. [37]

    Ge- ometric characteristics of the wasserstein metric on spd (n) and its applications on data processing.Entropy, 23(9):1214,

    Yihao Luo, Shiqiang Zhang, Yueqi Cao, and Huafei Sun. Ge- ometric characteristics of the wasserstein metric on spd (n) and its applications on data processing.Entropy, 23(9):1214,

    work page

  2. [1]

    The plenoptic function and the elements of early vision

    Edward H Adelson, James R Bergen, et al. The plenoptic function and the elements of early vision . Vision and Mod- eling Group, Media Laboratory, Massachusetts Institute of Technology, 1991. 2

    work page 1991

  3. [2]

    imghum: Implicit generative models of 3d human shape and articulated pose

    Thiemo Alldieck, Hongyi Xu, and Cristian Sminchisescu. imghum: Implicit generative models of 3d human shape and articulated pose. In ICCV, 2021. 2

    work page 2021

  4. [3]

    Gra- dient flows: in metric spaces and in the space of probability measures

    Luigi Ambrosio, Nicola Gigli, and Giuseppe Savar ´e. Gra- dient flows: in metric spaces and in the space of probability measures. Springer Science & Business Media, 2008. 1

    work page 2008

  5. [4]

    Rignerf: Fully controllable neu- ral 3d portraits

    ShahRukh Athar, Zexiang Xu, Kalyan Sunkavalli, Eli Shechtman, and Zhixin Shu. Rignerf: Fully controllable neu- ral 3d portraits. In CVPR, 2022. 2

    2022

  6. [5]

    HyperReel: High-fidelity 6-DoF video with ray- conditioned sampling

    Benjamin Attal, Jia-Bin Huang, Christian Richardt, Michael Zollhoefer, Johannes Kopf, Matthew O’Toole, and Changil Kim. HyperReel: High-fidelity 6-DoF video with ray- conditioned sampling. In Conference on Computer Vision and Pattern Recognition (CVPR), 2023. 2, 6, 8

    work page 2023

  7. [6]

    High-fidelity facial avatar reconstruction from monocular video with generative priors

    Yunpeng Bai, Yanbo Fan, Xuan Wang, Yong Zhang, Jingx- iang Sun, Chun Yuan, and Ying Shan. High-fidelity facial avatar reconstruction from monocular video with generative priors. In CVPR, 2023. 2

    work page 2023

  8. [7]

    Performance of optical flow techniques

    John L Barron, David J Fleet, and Steven S Beauchemin. Performance of optical flow techniques. International jour- nal of computer vision, 12:43–77, 1994. 9

    work page 1994

Show all 71 references
  1. [8]

    Simple online and realtime tracking

    Alex Bewley, Zeming Ge, David Ott, Fabio Ramos, and Ajay Upadhya. Simple online and realtime tracking. In2016 IEEE International Conference on Image Processing (ICIP), pages 3464–3468, 2016. 2

    2016

  2. [9]

    Regularized estimation of large covariance matrices

    Peter J Bickel and Elizaveta Levina. Regularized estimation of large covariance matrices. 2008. 4

    2008

  3. [10]

    Unstructured lumigraph ren- dering

    Chris Buehler, Michael Bosse, Leonard McMillan, Steven Gortler, and Michael Cohen. Unstructured lumigraph ren- dering. 2001. 2

    2001

  4. [11]

    Hexplane: A fast representa- tion for dynamic scenes

    Ang Cao and Justin Johnson. Hexplane: A fast representa- tion for dynamic scenes. CVPR, 2023. 2

    2023

  5. [12]

    Estimation, control, and the discrete Kalman filter

    Donald E Catlin. Estimation, control, and the discrete Kalman filter. Springer Science & Business Media, 2012. 1

    2012

  6. [13]

    Davison and et al

    Andrew J. Davison and et al. Monoslam: Real-time single camera slam. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2007. 2

    2007

  7. [14]

    4d-rotor gaussian splatting: towards efficient novel view synthesis for dynamic scenes

    Yuanxing Duan, Fangyin Wei, Qiyu Dai, Yuhang He, Wen- zheng Chen, and Baoquan Chen. 4d-rotor gaussian splatting: towards efficient novel view synthesis for dynamic scenes. In ACM SIGGRAPH 2024 Conference Papers , pages 1–11,

    2024

  8. [15]

    4d-rotor gaussian splatting: 11 Towards efficient novel view synthesis for dynamic scenes

    Yuanxing Duan, Fangyin Wei, Qiyu Dai, Yuhang He, Wen- zheng Chen, and Baoquan Chen. 4d-rotor gaussian splatting: 11 Towards efficient novel view synthesis for dynamic scenes. In Proc. SIGGRAPH, 2024. 6, 8

    2024

  9. [16]

    3d gaussian splatting as new era: A survey

    Ben Fei, Jingyi Xu, Rui Zhang, Qingyuan Zhou, Weidong Yang, and Ying He. 3d gaussian splatting as new era: A survey. IEEE Transactions on Visualization and Computer Graphics, 2024. 1

    2024

  10. [17]

    K-planes: Explicit radiance fields in space, time, and appearance

    Sara Fridovich-Keil, Giacomo Meanti, Frederik Rahbæk Warburg, Benjamin Recht, and Angjoo Kanazawa. K-planes: Explicit radiance fields in space, time, and appearance. In Proceedings of the IEEE/CVF Conference on Computer Vi- sion and Pattern Recognition, pages 12479–12488, 2023...

    2023

  11. [18]

    Dynamic view synthesis from dynamic monocular video

    Chen Gao, Ayush Saraf, Johannes Kopf, and Jia-Bin Huang. Dynamic view synthesis from dynamic monocular video. In ICCV, 2021. 2

    2021

  12. [19]

    G. H. Givens and R. W. Shortt. Class of wasserstein distances for probability measures on euclidean spaces. The Michigan Mathematical Journal, 31(2):231–240, 1984. 1, 4

    1984

  13. [20]

    Cayley, sylvester, and early matrix the- ory

    Nicholas J Higham. Cayley, sylvester, and early matrix the- ory. Linear Algebra Appl., 428:39–43, 2008. 5

    2008

  14. [21]

    Gauhuman: Articulated gaus- sian splatting from monocular human videos

    Shoukang Hu and Ziwei Liu. Gauhuman: Articulated gaus- sian splatting from monocular human videos. In CVPR,

  15. [22]

    Sc-gs: Sparse-controlled gaussian splatting for editable dynamic scenes

    Yi-Hua Huang, Yang-Tian Sun, Ziyi Yang, Xiaoyang Lyu, Yan-Pei Cao, and Xiaojuan Qi. Sc-gs: Sparse-controlled gaussian splatting for editable dynamic scenes. arXiv preprint arXiv:2312.14937, 2023. 2, 4

    2023 arXiv

  16. [23]

    A survey of dynamic 3d scene reconstruction

    MU Taijiang] [HUANG Jiahui. A survey of dynamic 3d scene reconstruction. Journal of Graphics, 45(1):14, 2024. 1

    2024

  17. [24]

    In- stantavatar: Learning avatars from monocular video in 60 seconds

    Tianjian Jiang, Xu Chen, Jie Song, and Otmar Hilliges. In- stantavatar: Learning avatars from monocular video in 60 seconds. In CVPR, 2023. 2

    2023

  18. [25]

    Rudolf E. Kalman. A new approach to linear filtering and prediction problems. Transactions of the ASME—Journal of Basic Engineering, 82(1):35–45, 1960. 3, 4

    1960

  19. [26]

    3d gaussian splatting for real-time radiance field rendering

    Bernhard Kerbl, Georgios Kopanas, Thomas Leimk ¨uhler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Transactions on Graphics, 42 (4), 2023. 1, 2

    2023

  20. [27]

    Adam: A method for Stochastic Optimization

    Diederik P Kingma and Jimmy Ba. Adam: A method for Stochastic Optimization. arXiv preprint arXiv:1412.6980 ,

    arXiv

  21. [28]

    Peak signal-to-noise ratio revisited: Is simple beautiful? In 2012 Fourth International Workshop on Quality of Multimedia Experience , pages 37–

    Jari Korhonen and Junyong You. Peak signal-to-noise ratio revisited: Is simple beautiful? In 2012 Fourth International Workshop on Quality of Multimedia Experience , pages 37–

    2012

  22. [29]

    Light field rendering

    M LEVOY . Light field rendering. 1996. 2

    1996

  23. [30]

    Streaming radiance fields for 3d video synthesis

    Lingzhi Li, Zhen Shen, zhongshu wang, Li Shen, and Ping Tan. Streaming radiance fields for 3d video synthesis. In Advances in Neural Information Processing Systems , 2022. 2, 6, 8

    2022

  24. [31]

    Neural 3d video synthesis from multi-view video

    Tianye Li, Mira Slavcheva, Michael Zollhoefer, Simon Green, Christoph Lassner, Changil Kim, Tanner Schmidt, Steven Lovegrove, Michael Goesele, Richard Newcombe, et al. Neural 3d video synthesis from multi-view video. In Proceedings of the IEEE/CVF Conference on Computer Vi- si...

    2022

  25. [32]

    Neural Scene Flow Fields for Space-time View Synthesis of Dynamic Scenes

    Zhengqi Li, Simon Niklaus, Noah Snavely, and Oliver Wang. Neural Scene Flow Fields for Space-time View Synthesis of Dynamic Scenes. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition, pages 6498–6508, 2021. 1

    2021

  26. [33]

    Spacetime gaus- sian feature splatting for real-time dynamic view synthesis

    Zhan Li, Zhang Chen, Zhong Li, and Yi Xu. Spacetime gaus- sian feature splatting for real-time dynamic view synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8508–8520, 2024. 1, 3

    2024

  27. [34]

    Neural vol- umes: Learning dynamic renderable volumes from images

    Stephen Lombardi, Tomas Simon, Jason Saragih, Gabriel Schwartz, Andreas Lehrmann, and Yaser Sheikh. Neural vol- umes: Learning dynamic renderable volumes from images. ACM Trans. Graph., 38(4):65:1–65:14, 2019. 2

    2019

  28. [35]

    3d geometry-aware deformable gaussian splatting for dynamic view synthesis

    Zhicheng Lu, Xiang Guo, Le Hui, Tianrui Chen, Min Yang, Xiao Tang, Feng Zhu, and Yuchao Dai. 3d geometry-aware deformable gaussian splatting for dynamic view synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8900–8910, 2024. 2

    2024

  29. [36]

    Dynamic 3d gaussians: Tracking by per- sistent dynamic view synthesis

    Jonathon Luiten, Georgios Kopanas, Bastian Leibe, and Deva Ramanan. Dynamic 3d gaussians: Tracking by per- sistent dynamic view synthesis. In 3DV, 2024. 1, 2, 3

    2024

  30. [38]

    Srinivasan, Rodrigo Ortiz-Cayon, Nima Khademi Kalantari, Ravi Ramamoorthi, Ren Ng, and Abhishek Kar

    Ben Mildenhall, Pratul P. Srinivasan, Rodrigo Ortiz-Cayon, Nima Khademi Kalantari, Ravi Ramamoorthi, Ren Ng, and Abhishek Kar. Local light field fusion: Practical view syn- thesis with prescriptive sampling guidelines. ACM Transac- tions on Graphics (TOG), 2019. 2

    2019

  31. [39]

    Nerf: Representing scenes as neural radiance fields for view synthesis

    B Mildenhall, PP Srinivasan, M Tancik, JT Barron, R Ra- mamoorthi, and R Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In ECCV, 2020. 1, 2

    2020

  32. [40]

    Statistical aspects of wasserstein distances

    Victor M Panaretos and Yoav Zemel. Statistical aspects of wasserstein distances. Annual review of statistics and its ap- plication, 6(1):405–431, 2019. 1, 4

    2019

  33. [41]

    Point-dynrf: Point- based dynamic radiance fields from a monocular video

    Byeongjun Park and Changick Kim. Point-dynrf: Point- based dynamic radiance fields from a monocular video. In 2024 IEEE/CVF Winter Conference on Applications of Com- puter Vision (WACV), pages 3159–3169, 2024. 1

    2024

  34. [42]

    Nerfies: Deformable neural radi- ance fields

    Jeong Joon Park and et al. Nerfies: Deformable neural radi- ance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 4480–4490,

  35. [43]

    Barron, Sofien Bouaziz, Dan B Goldman, Ricardo Martin- Brualla, and Steven M

    Keunhong Park, Utkarsh Sinha, Peter Hedman, Jonathan T. Barron, Sofien Bouaziz, Dan B Goldman, Ricardo Martin- Brualla, and Steven M. Seitz. Hypernerf: A higher- dimensional representation for topologically varying neural radiance fields. ACM Trans. Graph., 40(6), 2021. 1, 2

    2021

  36. [44]

    Ani- matable neural radiance fields for modeling dynamic human bodies

    Sida Peng, Junting Dong, Qianqian Wang, Shangzhan Zhang, Qing Shuai, Xiaowei Zhou, and Hujun Bao. Ani- matable neural radiance fields for modeling dynamic human bodies. In ICCV, 2021. 2 12

    2021

  37. [45]

    D-nerf: Neural radiance fields for dynamic scenes

    Albert Pumarola, Enric Corona, Gerard Pons-Moll, and Francesc Moreno-Noguer. D-nerf: Neural radiance fields for dynamic scenes. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition, pages 10318–10327, 2021. 2, 6

    2021

  38. [46]

    3dgs-avatar: Animatable avatars via deformable 3d gaussian splatting

    Zhiyin Qian, Shaofei Wang, Marko Mihajlovic, Andreas Geiger, and Siyu Tang. 3dgs-avatar: Animatable avatars via deformable 3d gaussian splatting. In CVPR, 2024. 2

    2024

  39. [47]

    Improving the convergence of dynamic nerfs via optimal transport

    Sameera Ramasinghe, Violetta Shevchenko, Gil Avraham, Hisham Husain, and Anton van den Hengel. Improving the convergence of dynamic nerfs via optimal transport. 2024. 2

    2024

  40. [48]

    Kalman- Net: Neural Network Aided Kalman Filtering for Partially Known Dynamics

    Guy Revach, Nir Shlezinger, Xiaoyong Ni, Adria Lopez Es- coriza, Ruud JG Van Sloun, and Yonina C Eldar. Kalman- Net: Neural Network Aided Kalman Filtering for Partially Known Dynamics. IEEE Transactions on Signal Processing, 70:1532–1547, 2022. 2

    2022

  41. [49]

    Free view synthesis

    Gernot Riegler and Vladlen Koltun. Free view synthesis. In ECCV, 2020. 2

    2020

  42. [50]

    Stable view synthesis

    Gernot Riegler and Vladlen Koltun. Stable view synthesis. In CVPR, 2021. 2

    2021

  43. [51]

    Tensor4d: Efficient neu- ral 4d decomposition for high-fidelity dynamic reconstruc- tion and rendering

    Ruizhi Shao, Zerong Zheng, Hanzhang Tu, Boning Liu, Hongwen Zhang, and Yebin Liu. Tensor4d: Efficient neu- ral 4d decomposition for high-fidelity dynamic reconstruc- tion and rendering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2023. 1

    2023

  44. [52]

    Nerf- player: A streamable dynamic scene representation with de- composed neural radiance fields

    Liangchen Song, Anpei Chen, Zhong Li, Zhang Chen, Lele Chen, Junsong Yuan, Yi Xu, and Andreas Geiger. Nerf- player: A streamable dynamic scene representation with de- composed neural radiance fields. IEEE Transactions on Vi- sualization and Computer Graphics, 2023. 2, 6, 8

    2023

  45. [53]

    Topics in optimal transportation

    C ´edric Villani. Topics in optimal transportation. American Mathematical Soc., 2021. 4

    2021

  46. [54]

    A self-supervised, differentiable kalman filter for uncertainty- aware visual-inertial odometry, 2022

    Brandon Wagstaff, Emmett Wise, and Jonathan Kelly. A self-supervised, differentiable kalman filter for uncertainty- aware visual-inertial odometry, 2022. 2

    2022

  47. [55]

    Deep learning-based 3d recon- struction from multiple images: A survey

    Chuhua Wang, Md Alimoor Reza, Vibhas Vats, Yingnan Ju, Nikhil Thakurdesai, Yuchen Wang, David J Crandall, Soon- heung Jung, and Jeongil Seo. Deep learning-based 3d recon- struction from multiple images: A survey. Neurocomputing, 597:128018, 2024. 1

    2024

  48. [56]

    Mixed neural voxels for fast multi- view video synthesis

    Feng Wang, Sinan Tan, Xinghang Li, Zeyue Tian, Yafei Song, and Huaping Liu. Mixed neural voxels for fast multi- view video synthesis. In Proceedings of the IEEE/CVF In- ternational Conference on Computer Vision (ICCV) , pages 19706–19716, 2023. 2, 8

    2023

  49. [57]

    Shape of motion: 4d reconstruc- tion from a single video, 2024

    Qianqian Wang, Vickie Ye, Hang Gao, Jake Austin, Zhengqi Li, and Angjoo Kanazawa. Shape of motion: 4d reconstruc- tion from a single video, 2024. 2

    2024

  50. [58]

    Image quality assessment: from error visibility to structural similarity

    Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Si- moncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600–612, 2004. 7

    2004

  51. [59]

    Hu- mannerf: Free-viewpoint rendering of moving people from monocular video

    Chung-Yi Weng, Brian Curless, Pratul P Srinivasan, Jonathan T Barron, and Ira Kemelmacher-Shlizerman. Hu- mannerf: Free-viewpoint rendering of moving people from monocular video. In CVPR, 2022. 2

    2022

  52. [60]

    4d gaussian splatting for real-time dynamic scene rendering

    Guanjun Wu, Taoran Yi, Jiemin Fang, Lingxi Xie, Xiaopeng Zhang, Wei Wei, Wenyu Liu, Qi Tian, and Xinggang Wang. 4d gaussian splatting for real-time dynamic scene rendering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20310–20320,...

    2024

  53. [61]

    4d gaussian splatting for real-time dynamic scene rendering

    Guanjun Wu, Taoran Yi, Jiemin Fang, Lingxi Xie, Xiaopeng Zhang, Wei Wei, Wenyu Liu, Qi Tian, and Wang Xinggang. 4d gaussian splatting for real-time dynamic scene rendering. In CVPR, 2024. 2

    2024

  54. [62]

    Dˆ 2nerf: Self-supervised decoupling of dynamic and static objects from a monocular video

    Tianhao Wu, Fangcheng Zhong, Andrea Tagliasacchi, For- rester Cole, and Cengiz Oztireli. Dˆ 2nerf: Self-supervised decoupling of dynamic and static objects from a monocular video. In NeurIPS, 2022. 2

    2022

  55. [63]

    Recent advances in 3d gaussian splatting

    Tong Wu, Yu-Jie Yuan, Ling-Xiao Zhang, Jie Yang, Yan- Pei Cao, Ling-Qi Yan, and Lin Gao. Recent advances in 3d gaussian splatting. Computational Visual Media, 10(4):613– 642, 2024. 1

    2024

  56. [64]

    Nerf-ds: Neural ra- diance fields for dynamic specular objects

    Zhiwen Yan, Chen Li, and Gim Hee Lee. Nerf-ds: Neural ra- diance fields for dynamic specular objects. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8285–8295, 2023. 1

    2023

  57. [65]

    Real- time photorealistic dynamic scene representation and render- ing with 4d gaussian splatting

    Zeyu Yang, Hongye Yang, Zijie Pan, and Li Zhang. Real- time photorealistic dynamic scene representation and render- ing with 4d gaussian splatting. In The Twelfth International Conference on Learning Representations. 1, 3, 6, 8

  58. [66]

    Deformable 3d gaussians for high-fidelity monocular dynamic scene reconstruction.arXiv preprint arXiv:2309.13101, 2023

    Ziyi Yang, Xinyu Gao, Wen Zhou, Shaohui Jiao, Yuqing Zhang, and Xiaogang Jin. Deformable 3d gaussians for high-fidelity monocular dynamic scene reconstruction.arXiv preprint arXiv:2309.13101, 2023. 2, 4

    2023 arXiv

  59. [67]

    Real- time photorealistic dynamic scene representation and render- ing with 4d gaussian splatting

    Zeyu Yang, Hongye Yang, Zijie Pan, and Li Zhang. Real- time photorealistic dynamic scene representation and render- ing with 4d gaussian splatting. In ICLR, 2023. 2

    2023

  60. [68]

    Deformable 3d gaussians for high- fidelity monocular dynamic scene reconstruction

    Ziyi Yang, Xinyu Gao, Wen Zhou, Shaohui Jiao, Yuqing Zhang, and Xiaogang Jin. Deformable 3d gaussians for high- fidelity monocular dynamic scene reconstruction. In Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 20331–20341, 2024. 1, 3, 6

    2024

  61. [69]

    Kfd-nerf: Kalman filter-based defor- mation field for dynamic neural radiance fields

    Yifan Zhan and et al. Kfd-nerf: Kalman filter-based defor- mation field for dynamic neural radiance fields. In Proceed- ings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023. 2

    2023

  62. [70]

    Gaussiancube: Structuring gaussian splatting using optimal transport for 3d generative modeling

    Bowen Zhang, Yiji Cheng, Jiaolong Yang, Chunyu Wang, Feng Zhao, Yansong Tang, Dong Chen, and Baining Guo. Gaussiancube: Structuring gaussian splatting using optimal transport for 3d generative modeling. In Advances in Neural Information Processing Systems, 2024. 2

    2024

  63. [71]

    The unreasonable effectiveness of deep features as a perceptual metric

    Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shecht- man, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recogni- tion, pages 586–595, 2018. 7 13

    2018

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.