pith. sign in

arxiv: 2606.29453 · v2 · pith:JGUGKJKLnew · submitted 2026-06-28 · 💻 cs.CV · cs.AI· cs.GR

Resonant Brane Splatting for Arbitrary-Scale Super-Resolution

Giulio Federico , Giuseppe Amato , Claudio Gennaro , Fabio Carrara , Marco Di Benedetto This is my paper

Pith reviewed 2026-07-03 22:43 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.GR
keywords arbitrary-scale super-resolutionGaussian splattingHermite modesdifferentiable renderingexplicit primitivesimage reconstructionfeed-forward networks
0
0 comments X

The pith

Branes augment Gaussians with Hermite modes so each primitive models textures without needing many overlaps in arbitrary-scale super-resolution.

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

The paper introduces Resonant Brane Splatting to handle continuous magnification factors in image reconstruction more efficiently than prior Gaussian splatting techniques. It replaces simple Gaussian primitives with Branes that layer higher-order Gaussian-Hermite modes inside the envelope, each with its own color coefficient, so a single footprint can represent edges and fine detail. Brane parameters are predicted from low-resolution input features in one forward pass. A differentiable rasterizer then applies quantum turning point culling to skip regions whose contribution is negligible. On standard benchmarks this yields higher reconstruction quality and a better speed-quality balance than both implicit neural methods and earlier explicit Gaussian splatting baselines.

Core claim

Resonant Brane Splatting replaces flat Gaussians with Branes that augment the standard Gaussian envelope with internal Gaussian-Hermite modes, each assigned a distinct color coefficient. The zero-order mode recovers ordinary Gaussian splatting while higher-order modes capture high frequencies. Parameters are predicted directly from low-resolution features. Because each Brane is mathematically richer, far fewer primitives need to overlap at any target pixel. An efficient fully differentiable rasterizer exploits this with a precise culling strategy based on the classical quantum turning point, safely skipping negligible regions and thereby reducing rendering overhead.

What carries the argument

Branes: Gaussian envelopes augmented with internal Gaussian-Hermite modes that each carry an independent color coefficient

If this is right

  • Fewer Branes need to overlap to reconstruct each target pixel than standard Gaussians require.
  • The rasterizer can safely cull larger regions without visible degradation.
  • Direct prediction of Brane parameters supports true feed-forward inference at any continuous scale.
  • Reconstruction quality improves over both implicit decoders and prior Gaussian splatting methods on ASR benchmarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same mode-augmented primitives could reduce primitive counts in other explicit rendering pipelines that currently rely on dense Gaussian overlaps.
  • Increasing the maximum Hermite mode order would trade parameter count for even lower overlap density, a knob the current work leaves for later tuning.
  • The quantum turning point culling rule may transfer directly to other Gaussian-based representations in computer vision once the envelope is similarly enriched.

Load-bearing premise

That adding internal Gaussian-Hermite modes lets far fewer primitives overlap while still modeling local contrast and complex textures accurately, and that quantum-turning-point culling introduces negligible error.

What would settle it

Render the same high-magnification test image with RBS and with a standard Gaussian splatting baseline using ten times as many primitives; visible high-frequency artifacts unique to the RBS output would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.29453 by Claudio Gennaro, Fabio Carrara, Giulio Federico, Giuseppe Amato, Marco Di Benedetto.

Figure 1
Figure 1. Figure 1: Resonant Brane Splatting Overview. Given an LR input and scale factor, a backbone extracts a feature map de￾coded into our proposed Brane primitives, composing a continu￾ous Brane field. Increasing primitive count and Brane complexity better models SR outputs. Conversely, degree-0 Branes (Gaussian Splatting) yield blurry results under equal primitive budgets. While flexible, INRs require dense pixel-wise q… view at source ↗
Figure 2
Figure 2. Figure 2: Brane Expressiveness. Left: Cropped ground truth. Right: Reconstructions varying the number of Branes (K) and Gaussian￾Hermite degrees (N, M), where N = M = 0 corresponds to standard Gaussian Splatting. Please zoom in for details. 3. Method 3.1. Limitations of Splatting-Based ASR Given a low-resolution input image ILR ∈ R H×W×3 and a continuous target scale factor s ∈ R +, Arbitrary￾Scale Super-Resolution … view at source ↗
Figure 3
Figure 3. Figure 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of Brane parameters. Mode colors control the internal appearance of the primitive, while footprint and opacity control where and how strongly the Brane contributes [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rasterization and culling strategies. Decoded LR features form a continuous Brane space where the sampling grid resolution dictates the SR output resolution (left). Given a red target pixel, we efficiently determine its final color by discarding primitives located outside the bounding box dmax and omitting those with negligible contributions beyond the quantum turning point Rmax (right). Culling Branes. De… view at source ↗
Figure 6
Figure 6. Figure 6: Impact of Brane degree. Unlike standard Gaussians (N = M = 0) that blur intricate details, higher order modes (N = M ∈ {2, 3, 5, 7}) synthesize sharper features, progressively revealing complex textures and vibrant colors. protocol fixes the HR ground-truth size, larger upsampling scales correspond to smaller LR inputs. As a result, back￾bone cost and, for splatting methods, the number of raster￾ized primi… view at source ↗
Figure 7
Figure 7. Figure 7: Brane morphology and distribution (N = M = 5). Left: Activation map (opacity-weighted sum of higher-order color magnitudes); active modes emerge on intricate details, collapsing to standard Gaussians in flat areas. Center: Primitives clustering along high-frequency edges. Right: Isolated splats revealing indi￾vidual color and structural complexity. minimal overhead when using one primitive per LR pixel, as… view at source ↗
Figure 8
Figure 8. Figure 8: Qualitative results. Visual comparison between RBS and several competing methods across different scale factors, using RDN [58] as the backbone network. Detailed results for each model are provided in the supplementary material. Hermite degree. The degrees (N, M) define Brane ca￾pacity, with N = M = 0 matching a standard Gaussian. At severe scales, the LR input lacks sufficient high-frequency information t… view at source ↗
read the original abstract

Arbitrary-Scale Super-Resolution (ASR) reconstructs images at continuous magnification factors. Recent methods accelerate inference by replacing computationally heavy implicit neural decoders with explicit 2D Gaussian Splatting (GS). However, since standard Gaussians are smooth low-pass primitives, modeling edges and fine textures requires multiple overlapping, well-aligned splats, which creates severe bottlenecks during rasterization. To address this, we introduce Resonant Brane Splatting (RBS), a feed-forward ASR framework. RBS replaces flat Gaussians with Branes: expressive primitives that emit spatially varying colors to natively model local contrast and complex textures within a single footprint. We achieve this by augmenting the standard Gaussian envelope with internal Gaussian-Hermite modes, assigning a distinct color coefficient to each. The zero-order mode recovers standard GS, while higher-order modes capture high frequencies. We predict Brane parameters directly from low-resolution features. Because Branes provide a mathematically richer formulation than simple Gaussians, far fewer primitives need to overlap to reconstruct a given target pixel. To exploit this, we introduce an efficient fully differentiable rasterizer with a precise culling strategy based on the classical quantum turning point. This allows us to safely skip negligible regions, drastically reducing the rendering overhead. Experiments on standard ASR benchmarks show that RBS improves reconstruction quality over implicit and GS baselines, while achieving superior speed-quality trade-off than prior GS methods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Resonant Brane Splatting (RBS), a feed-forward framework for arbitrary-scale super-resolution (ASR). It replaces standard 2D Gaussians with Branes formed by augmenting a Gaussian envelope with internal Gaussian-Hermite modes, each assigned a distinct color coefficient, to model local contrast and textures within a single footprint. Brane parameters are predicted from low-resolution features; a fully differentiable rasterizer employs quantum-turning-point culling to skip negligible regions. The central claim is that RBS yields higher reconstruction quality than implicit and Gaussian-splatting baselines while providing a superior speed-quality trade-off on standard ASR benchmarks.

Significance. If the empirical results and error bounds hold, the work could meaningfully advance explicit splatting approaches to ASR by increasing per-primitive expressiveness, thereby reducing the number of overlapping primitives required. The combination of Hermite modes with turning-point culling is a distinctive technical contribution, though its practical impact hinges on reproducible quantitative validation and a rigorous bound on accumulated culling error.

major comments (2)
  1. [Abstract] Abstract: the central empirical claim of improved quality and superior speed-quality trade-off is asserted without any quantitative metrics, tables, error bars, ablation details, or dataset splits, rendering the claim unverifiable from the supplied text and directly undermining soundness assessment.
  2. [Method (culling strategy)] Method (culling strategy): the 2-D extension of the quantum-turning-point rule to a sum of Hermite-weighted Gaussians is not shown to bound integrated radiance error over a pixel footprint once the magnification factor is continuous; coherent addition of discarded tails from neighboring Branes at high frequencies could eliminate the claimed speed advantage. This is load-bearing for the efficiency claim.
minor comments (2)
  1. [Abstract] Abstract: the number of Hermite modes and per-mode color coefficients are introduced as free parameters predicted from data, yet no grounding, typical values, or sensitivity analysis is supplied.
  2. [Abstract] Abstract: the term 'Brane' is used without an explicit definition or reference to its mathematical origin within the manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central empirical claim of improved quality and superior speed-quality trade-off is asserted without any quantitative metrics, tables, error bars, ablation details, or dataset splits, rendering the claim unverifiable from the supplied text and directly undermining soundness assessment.

    Authors: We agree that the abstract states the empirical claims qualitatively without supporting numbers. In the revised manuscript we will expand the abstract to include concrete quantitative highlights drawn from the experiments section, such as PSNR/SSIM gains versus implicit and Gaussian-splatting baselines on standard ASR benchmarks together with runtime comparisons and a brief note on the dataset splits used. revision: yes

  2. Referee: [Method (culling strategy)] Method (culling strategy): the 2-D extension of the quantum-turning-point rule to a sum of Hermite-weighted Gaussians is not shown to bound integrated radiance error over a pixel footprint once the magnification factor is continuous; coherent addition of discarded tails from neighboring Branes at high frequencies could eliminate the claimed speed advantage. This is load-bearing for the efficiency claim.

    Authors: The current manuscript presents the 2-D culling rule as a direct extension of the classical quantum turning point applied to the Gaussian envelope, with higher-order Hermite modes treated as bounded perturbations inside that envelope. However, we acknowledge that an explicit analytic bound on the integrated radiance error for arbitrary continuous magnification factors, including an analysis of possible coherent summation of discarded high-frequency tails across neighboring Branes, is not derived. We will add a dedicated subsection containing the error-bound derivation and supporting numerical validation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method introduces new primitives and culling rule without reducing to self-definition or fitted inputs.

full rationale

The paper defines Branes as an augmentation of the Gaussian envelope with Gaussian-Hermite modes and assigns color coefficients per mode, then predicts parameters from low-resolution features as the core of the feed-forward model. The culling rule is imported from classical quantum mechanics (turning point) rather than derived from the paper's own fitted values. No equations reduce a claimed prediction to its own inputs by construction, no self-citation chains justify uniqueness, and no ansatz is smuggled via prior work. Experiments report empirical gains on benchmarks, keeping the derivation self-contained against external data.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The approach rests on the domain assumption that Hermite-augmented primitives are richer than Gaussians, plus several free parameters for mode count and coefficients that are predicted from features but still require training.

free parameters (2)
  • number of Hermite modes
    Chosen to balance expressiveness against rasterization cost; value not stated in abstract.
  • per-mode color coefficients
    Distinct coefficient assigned to each mode; fitted during training from low-resolution features.
axioms (1)
  • domain assumption Branes provide a mathematically richer formulation than simple Gaussians allowing fewer overlaps
    Invoked to justify reduced rendering overhead.
invented entities (1)
  • Brane no independent evidence
    purpose: Expressive splat primitive that emits spatially varying colors via Gaussian-Hermite modes
    Newly postulated to overcome smoothness limits of standard Gaussians; no independent evidence supplied.

pith-pipeline@v0.9.1-grok · 5791 in / 1246 out tokens · 21521 ms · 2026-07-03T22:43:05.629940+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    Low-complexity single-image super-resolution based on nonnegative neighbor embedding

    Marco Bevilacqua, Aline Roumy, Christine Guillemot, and Marie Line Alberi-Morel. Low-complexity single-image super-resolution based on nonnegative neighbor embedding

    work page

  2. [2]

    Ciaosr: Continuous implicit attention-in- attention network for arbitrary-scale image super-resolution

    Jiezhang Cao, Qin Wang, Yongqin Xian, Yawei Li, Bingbing Ni, Zhiming Pi, Kai Zhang, Yulun Zhang, Radu Timofte, and Luc Van Gool. Ciaosr: Continuous implicit attention-in- attention network for arbitrary-scale image super-resolution. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1796–1807, 2023. 1, 2, 5

    work page 2023

  3. [3]

    Ssl: A self-similarity loss for improving generative image super- resolution

    Du Chen, Zhengqiang Zhang, Jie Liang, and Lei Zhang. Ssl: A self-similarity loss for improving generative image super- resolution. InProceedings of the 32nd ACM International Conference on Multimedia, pages 3189–3198, 2024. 2

    work page 2024

  4. [4]

    Generalized and efficient 2d gaussian splatting for arbitrary- scale super-resolution

    Du Chen, Liyi Chen, Zhengqiang Zhang, and Lei Zhang. Generalized and efficient 2d gaussian splatting for arbitrary- scale super-resolution. InProceedings of the IEEE/CVF In- ternational Conference on Computer Vision (ICCV), pages 26435–26445, 2025. 1, 2, 3, 5, 6

    work page 2025

  5. [5]

    Beyond gaussians: Fast and high-fidelity 3d splatting with linear kernels

    Haodong Chen, Runnan Chen, Qiang Qu, Zhaoqing Wang, Tongliang Liu, Xiaoming Chen, and Yuk Ying Chung. Be- yond gaussians: Fast and high-fidelity 3d splatting with lin- ear kernels.arXiv preprint arXiv:2411.12440, 2024. 2

    work page arXiv 2024

  6. [6]

    Cascaded local implicit transformer for arbitrary-scale super-resolution

    Hao-Wei Chen, Yu-Syuan Xu, Min-Fong Hong, Yi-Min Tsai, Hsien-Kai Kuo, and Chun-Yi Lee. Cascaded local implicit transformer for arbitrary-scale super-resolution. In Proceedings of the IEEE/CVF Conference on Computer Vi- sion and Pattern Recognition (CVPR), pages 18257–18267,

    work page

  7. [7]

    Hat: Hybrid attention transformer for image restoration.IEEE Transac- tions on Pattern Analysis and Machine Intelligence, 48(3): 2676–2694, 2026

    Xiangyu Chen, Xintao Wang, Wenlong Zhang, Xiangtao Kong, Yu Qiao, Jiantao Zhou, and Chao Dong. Hat: Hybrid attention transformer for image restoration.IEEE Transac- tions on Pattern Analysis and Machine Intelligence, 48(3): 2676–2694, 2026. 7

    work page 2026

  8. [8]

    Learning continuous image representation with local implicit image function

    Yinbo Chen, Sifei Liu, and Xiaolong Wang. Learning continuous image representation with local implicit image function. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8628–8638,

    work page

  9. [9]

    A general expression for hermite expansions with applications.The Mathematics Enthusiast, 21(1):71– 87, 2024

    Tom P Davis. A general expression for hermite expansions with applications.The Mathematics Enthusiast, 21(1):71– 87, 2024. 3

    work page 2024

  10. [10]

    Simoncelli

    Keyan Ding, Kede Ma, Shiqi Wang, and Eero P. Simoncelli. Image quality assessment: Unifying structure and texture similarity.IEEE Transactions on Pattern Analysis and Ma- chine Intelligence, 44(5):2567–2581, 2022. 5

    work page 2022

  11. [11]

    Learning a deep convolutional network for image super-resolution

    Chao Dong, Chen Change Loy, Kaiming He, and Xiaoou Tang. Learning a deep convolutional network for image super-resolution. InEuropean conference on computer vi- sion, pages 184–199. Springer, 2014. 2

    work page 2014

  12. [12]

    Accel- erating the super-resolution convolutional neural network

    Chao Dong, Chen Change Loy, and Xiaoou Tang. Accel- erating the super-resolution convolutional neural network. InComputer Vision – ECCV 2016, pages 391–407, Cham,

    work page 2016

  13. [13]

    Springer International Publishing. 5

    work page

  14. [14]

    Acceler- ating the super-resolution convolutional neural network

    Chao Dong, Chen Change Loy, and Xiaoou Tang. Acceler- ating the super-resolution convolutional neural network. In European conference on computer vision, pages 391–407. Springer, 2016. 2

    work page 2016

  15. [15]

    M theory (the theory formerly known as strings)

    Michael J Duff. M theory (the theory formerly known as strings). InThe World in Eleven Dimensions, pages 416–

    work page

  16. [16]

    Ges : Generalized exponential splatting for efficient radiance field rendering

    Abdullah Hamdi, Luke Melas-Kyriazi, Jinjie Mai, Guocheng Qian, Ruoshi Liu, Carl V ondrick, Bernard Ghanem, and Andrea Vedaldi. Ges : Generalized exponential splatting for efficient radiance field rendering. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 19812–19822, 2024. 2

    work page 2024

  17. [17]

    Latent modulated function for com- putational optimal continuous image representation

    Zongyao He and Zhi Jin. Latent modulated function for com- putational optimal continuous image representation. InPro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 26026–26035, 2024. 1, 2, 5

    work page 2024

  18. [18]

    3d con- vex splatting: Radiance field rendering with 3d smooth con- vexes

    Jan Held, Renaud Vandeghen, Abdullah Hamdi, Adrien Deliege, Anthony Cioppa, Silvio Giancola, Andrea Vedaldi, Bernard Ghanem, and Marc Van Droogenbroeck. 3d con- vex splatting: Radiance field rendering with 3d smooth con- vexes. InProceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition (CVPR), pages 21360– 21369, 2025. 2

    work page 2025

  19. [19]

    Gaussiansr: High fidelity 2d gaussian splatting for arbitrary-scale image super-resolution

    Jintong Hu, Bin Xia, Bin Chen, Wenming Yang, and Lei Zhang. Gaussiansr: High fidelity 2d gaussian splatting for arbitrary-scale image super-resolution. InProceedings of the AAAI Conference on Artificial Intelligence, pages 3554– 3562, 2025. 1, 2, 5, 6

    work page 2025

  20. [20]

    Meta-sr: A magnification- arbitrary network for super-resolution

    Xuecai Hu, Haoyuan Mu, Xiangyu Zhang, Zilei Wang, Tieniu Tan, and Jian Sun. Meta-sr: A magnification- arbitrary network for super-resolution. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1575–1584, 2019. 1, 2, 5

    work page 2019

  21. [21]

    Sin- gle image super-resolution from transformed self-exemplars

    Jia-Bin Huang, Abhishek Singh, and Narendra Ahuja. Sin- gle image super-resolution from transformed self-exemplars. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015. 5, 7

    work page 2015

  22. [22]

    Deformable radial kernel splatting

    Yi-Hua Huang, Ming-Xian Lin, Yang-Tian Sun, Ziyi Yang, Xiaoyang Lyu, Yan-Pei Cao, and Xiaojuan Qi. Deformable radial kernel splatting. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 21513–21523, 2025. 2

    work page 2025

  23. [23]

    Grape (gaussian ren- dering for accelerated pixel enhancement) brings fast and lightweight arbitrary super-resolution

    Jung In Jang and Kyong Hwan Jin. Grape (gaussian ren- dering for accelerated pixel enhancement) brings fast and lightweight arbitrary super-resolution. InProceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 7750–7758, 2026. 2, 5, 6

    work page 2026

  24. [24]

    The weighted hermite polynomials form a basis for l 2 (R).The American Mathematical Monthly, 121(3):249–253, 2014

    William Johnston. The weighted hermite polynomials form a basis for l 2 (R).The American Mathematical Monthly, 121(3):249–253, 2014. 3

    work page 2014

  25. [25]

    3d gaussian splatting for real-time radiance field rendering.ACM Trans

    Bernhard Kerbl, Georgios Kopanas, Thomas Leimk ¨uhler, George Drettakis, et al. 3d gaussian splatting for real-time radiance field rendering.ACM Trans. Graph., 42(4):139–1,

    work page

  26. [26]

    Accurate image super-resolution using very deep convolutional net- 9 works

    Jiwon Kim, Jung Kwon Lee, and Kyoung Mu Lee. Accurate image super-resolution using very deep convolutional net- 9 works. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016. 2

    work page 2016

  27. [27]

    Deeply- recursive convolutional network for image super-resolution

    Jiwon Kim, Jung Kwon Lee, and Kyoung Mu Lee. Deeply- recursive convolutional network for image super-resolution. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 1637–1645, 2016

    work page 2016

  28. [28]

    Deep laplacian pyramid networks for fast and accurate super-resolution

    Wei-Sheng Lai, Jia-Bin Huang, Narendra Ahuja, and Ming- Hsuan Yang. Deep laplacian pyramid networks for fast and accurate super-resolution. InProceedings of the IEEE con- ference on computer vision and pattern recognition, pages 624–632, 2017. 2

    work page 2017

  29. [29]

    Deblurring 3d gaussian splatting

    Byeonghyeon Lee, Howoong Lee, Xiangyu Sun, Usman Ali, and Eunbyung Park. Deblurring 3d gaussian splatting. InComputer Vision – ECCV 2024, pages 127–143, Cham,

    work page 2024

  30. [30]

    Springer Nature Switzerland. 2

    work page

  31. [31]

    Local texture estima- tor for implicit representation function

    Jaewon Lee and Kyong Hwan Jin. Local texture estima- tor for implicit representation function. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1929–1938, 2022. 1, 2, 5

    work page 1929

  32. [32]

    Ls- dir: A large scale dataset for image restoration

    Yawei Li, Kai Zhang, Jingyun Liang, Jiezhang Cao, Ce Liu, Rui Gong, Yulun Zhang, Hao Tang, Yun Liu, Denis Deman- dolx, Rakesh Ranjan, Radu Timofte, and Luc Van Gool. Ls- dir: A large scale dataset for image restoration. InProceed- ings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pages 1775–1787,

    work page

  33. [33]

    Feedback network for image super- resolution

    Zhen Li, Jinglei Yang, Zheng Liu, Xiaomin Yang, Gwang- gil Jeon, and Wei Wu. Feedback network for image super- resolution. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019. 2

    work page 2019

  34. [34]

    Swinir: Image restoration us- ing swin transformer

    Jingyun Liang, Jiezhang Cao, Guolei Sun, Kai Zhang, Luc Van Gool, and Radu Timofte. Swinir: Image restoration us- ing swin transformer. InProceedings of the IEEE/CVF Inter- national Conference on Computer Vision (ICCV) Workshops, pages 1833–1844, 2021. 2

    work page 2021

  35. [35]

    Details or artifacts: A locally discriminative learning approach to realistic im- age super-resolution

    Jie Liang, Hui Zeng, and Lei Zhang. Details or artifacts: A locally discriminative learning approach to realistic im- age super-resolution. InProceedings of the IEEE/CVF con- ference on computer vision and pattern recognition, pages 5657–5666, 2022. 2

    work page 2022

  36. [36]

    Enhanced deep residual networks for single image super-resolution

    Bee Lim, Sanghyun Son, Heewon Kim, Seungjun Nah, and Kyoung Mu Lee. Enhanced deep residual networks for single image super-resolution. InProceedings of the IEEE Confer- ence on Computer Vision and Pattern Recognition (CVPR) Workshops, 2017. 5, 7

    work page 2017

  37. [37]

    Deformable beta splatting

    Rong Liu, Dylan Sun, Meida Chen, Yue Wang, and Andrew Feng. Deformable beta splatting. InProceedings of the Spe- cial Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers, New York, NY , USA, 2025. Association for Computing Machinery. 2

    work page 2025

  38. [38]

    Martin, C

    D. Martin, C. Fowlkes, D. Tal, and J. Malik. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecolog- ical statistics. InProceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, pages 416–423 vol.2, 2001. 5

    work page 2001

  39. [39]

    Sketch-based manga retrieval using manga109 dataset.Mul- timedia tools and applications, 76(20):21811–21838, 2017

    Yusuke Matsui, Kota Ito, Yuji Aramaki, Azuma Fujimoto, Toru Ogawa, Toshihiko Yamasaki, and Kiyoharu Aizawa. Sketch-based manga retrieval using manga109 dataset.Mul- timedia tools and applications, 76(20):21811–21838, 2017. 5

    work page 2017

  40. [40]

    Pixel to gaussian: Ultra-fast continuous super-resolution with 2d gaussian modeling.arXiv preprint arXiv:2503.06617, 2025

    Long Peng, Anran Wu, Wenbo Li, Peizhe Xia, Xueyuan Dai, Xinjie Zhang, Xin Di, Haoze Sun, Renjing Pei, Yang Wang, et al. Pixel to gaussian: Ultra-fast continuous super-resolution with 2d gaussian modeling.arXiv preprint arXiv:2503.06617, 2025. 2, 5, 6

    work page arXiv 2025

  41. [41]

    Dirichlet branes and ramond-ramond charges.Physical Review Letters, 75(26):4724, 1995

    Joseph Polchinski. Dirichlet branes and ramond-ramond charges.Physical Review Letters, 75(26):4724, 1995. 2

    work page 1995

  42. [42]

    Cambridge university press, 2020

    Jun John Sakurai and Jim Napolitano.Modern quantum me- chanics. Cambridge university press, 2020. 2, 3, 5

    work page 2020

  43. [43]

    Ntire 2017 challenge on single image super-resolution: Methods and results

    Radu Timofte, Eirikur Agustsson, Luc Van Gool, Ming- Hsuan Yang, and Lei Zhang. Ntire 2017 challenge on single image super-resolution: Methods and results. InProceed- ings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2017. 5, 7

    work page 2017

  44. [44]

    Learning a single net- work for scale-arbitrary super-resolution

    Longguang Wang, Yingqian Wang, Zaiping Lin, Jungang Yang, Wei An, and Yulan Guo. Learning a single net- work for scale-arbitrary super-resolution. InProceedings of the IEEE/CVF international conference on computer vision, pages 4801–4810, 2021. 2

    work page 2021

  45. [45]

    Esrgan: En- hanced super-resolution generative adversarial networks

    Xintao Wang, Ke Yu, Shixiang Wu, Jinjin Gu, Yihao Liu, Chao Dong, Yu Qiao, and Chen Change Loy. Esrgan: En- hanced super-resolution generative adversarial networks. In Proceedings of the European conference on computer vision (ECCV) workshops, pages 0–0, 2018. 2

    work page 2018

  46. [46]

    Bovik, H.R

    Zhou Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli. Image quality assessment: from error visibility to structural similarity.IEEE Transactions on Image Processing, 13(4): 600–612, 2004. 5

    work page 2004

  47. [47]

    Super-resolution neural oper- ator

    Min Wei and Xuesong Zhang. Super-resolution neural oper- ator. InProceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition (CVPR), pages 18247– 18256, 2023. 1, 2, 5

    work page 2023

  48. [48]

    String theory dynamics in various dimen- sions.Nuclear Physics B, 443(1-2):85–126, 1995

    Edward Witten. String theory dynamics in various dimen- sions.Nuclear Physics B, 443(1-2):85–126, 1995. 2

    work page 1995

  49. [49]

    Seesr: Towards semantics- aware real-world image super-resolution

    Rongyuan Wu, Tao Yang, Lingchen Sun, Zhengqiang Zhang, Shuai Li, and Lei Zhang. Seesr: Towards semantics- aware real-world image super-resolution. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 25456–25467, 2024. 2

    work page 2024

  50. [50]

    Im- plicit transformer network for screen content image contin- uous super-resolution

    Jingyu Yang, Sheng Shen, Huanjing Yue, and Kun Li. Im- plicit transformer network for screen content image contin- uous super-resolution. InAdvances in Neural Information Processing Systems, pages 13304–13315. Curran Associates, Inc., 2021. 2

    work page 2021

  51. [51]

    Local implicit normalizing flow for arbitrary-scale image super-resolution

    Jie-En Yao, Li-Yuan Tsao, Yi-Chen Lo, Roy Tseng, Chia- Che Chang, and Chun-Yi Lee. Local implicit normalizing flow for arbitrary-scale image super-resolution. InProceed- ings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 1776–1785, 2023. 1, 2, 5

    work page 2023

  52. [52]

    Fine-structure preserved real-world im- age super-resolution via transfer vae training

    Qiaosi Yi, Shuai Li, Rongyuan Wu, Lingchen Sun, Yuhui Wu, and Lei Zhang. Fine-structure preserved real-world im- age super-resolution via transfer vae training. InProceed- ings of the IEEE/CVF international conference on computer vision, pages 12415–12426, 2025. 2 10

    work page 2025

  53. [53]

    Scaling up to excellence: Practicing model scaling for photo- realistic image restoration in the wild

    Fanghua Yu, Jinjin Gu, Zheyuan Li, Jinfan Hu, Xiangtao Kong, Xintao Wang, Jingwen He, Yu Qiao, and Chao Dong. Scaling up to excellence: Practicing model scaling for photo- realistic image restoration in the wild. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 25669–25680, 2024. 2

    work page 2024

  54. [54]

    2dgh: 2d gaussian-hermite splatting for high-quality render- ing and better geometry features.IEEE Transactions on Visu- alization and Computer Graphics, 32(2):1513–1524, 2026

    Ruihan Yu, Tianyu Huang, Jingwang Ling, and Feng Xu. 2dgh: 2d gaussian-hermite splatting for high-quality render- ing and better geometry features.IEEE Transactions on Visu- alization and Computer Graphics, 32(2):1513–1524, 2026. 2, 4

    work page 2026

  55. [55]

    On single image scale-up using sparse-representations

    Roman Zeyde, Michael Elad, and Matan Protter. On single image scale-up using sparse-representations. InCurves and Surfaces, pages 711–730, Berlin, Heidelberg, 2012. Springer Berlin Heidelberg. 5

    work page 2012

  56. [56]

    Transcending the limit of local window: Ad- vanced super-resolution transformer with adaptive token dic- tionary

    Leheng Zhang, Yawei Li, Xingyu Zhou, Xiaorui Zhao, and Shuhang Gu. Transcending the limit of local window: Ad- vanced super-resolution transformer with adaptive token dic- tionary. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2856–2865,

    work page

  57. [57]

    Efros, Eli Shecht- man, and Oliver Wang

    Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shecht- man, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. InProceedings of the IEEE Conference on Computer Vision and Pattern Recogni- tion (CVPR), 2018. 5

    work page 2018

  58. [58]

    Efficient long-range attention network for image super- resolution

    Xindong Zhang, Hui Zeng, Shi Guo, and Lei Zhang. Efficient long-range attention network for image super- resolution. InEuropean conference on computer vision, pages 649–667. Springer, 2022. 2

    work page 2022

  59. [59]

    Image super-resolution using very deep residual channel attention networks

    Yulun Zhang, Kunpeng Li, Kai Li, Lichen Wang, Bineng Zhong, and Yun Fu. Image super-resolution using very deep residual channel attention networks. InProceedings of the European conference on computer vision (ECCV), pages 286–301, 2018. 2

    work page 2018

  60. [60]

    Residual dense network for image super-resolution

    Yulun Zhang, Yapeng Tian, Yu Kong, Bineng Zhong, and Yun Fu. Residual dense network for image super-resolution. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 2472–2481, 2018. 2, 5, 6, 7, 8 11

    work page 2018