arxiv: 2604.21984 · v2 · submitted 2026-04-23 · 💻 cs.CV

Recognition: unknown

Soft Anisotropic Diagrams for Differentiable Image Representation

Laki Iinbor , Zhiyang Dou , Wojciech Matusik

Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:41 UTC · model grok-4.3

classification 💻 cs.CV

keywords Soft Anisotropic DiagramsDifferentiable Image RepresentationAnisotropic Voronoi DiagramsExplicit RepresentationsTop-K PropagationImage ReconstructionNeural RenderingApollonius Diagrams

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The pith

Soft Anisotropic Diagrams represent images explicitly with adaptive sites, anisotropic metrics, and top-K softmax blending to deliver faster training and higher quality than prior explicit methods.

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

The paper introduces Soft Anisotropic Diagrams as an explicit differentiable image representation built from adaptive sites in the plane. Each site carries an anisotropic metric and an additively weighted distance; pixel colors arise from a softmax blend over a small per-pixel top-K subset of sites. This construction yields a soft anisotropic additively weighted Voronoi partition whose per-site temperatures remain learnable, preserving gradients while producing content-aligned boundaries. Rendering stays efficient because a maintained top-K map approximates the shading scores and is updated via jump-flooding propagation plus stochastic injection. The resulting pipeline trains faster than Image-GS and Instant-NGP while reaching higher PSNR at matched bitrate on standard benchmarks.

Core claim

Soft Anisotropic Diagrams (SAD) constitute an explicit and differentiable image representation in which each adaptive site defines an anisotropic metric together with an additively weighted distance score; pixel values are obtained by softmax blending over a fixed-size per-pixel top-K subset of sites, thereby inducing a soft Apollonius diagram with learnable temperatures that supports both clear boundaries and informative gradients.

What carries the argument

The soft anisotropic additively weighted Voronoi partition (Apollonius diagram) induced by sites with anisotropic metrics and additively weighted distances, realized through per-query top-K softmax blending and jump-flooding top-K propagation.

If this is right

Enables direct integration into differentiable pipelines for both forward rendering and inverse problems such as optimization or editing.
Supports fast random access and compact storage through the explicit site list and per-pixel top-K map.
Achieves 4-19 times end-to-end training speedups over state-of-the-art baselines while maintaining or improving PSNR at matched bitrate.
Delivers 46.0 dB PSNR on Kodak images in 2.2 seconds of encoding, versus 28 seconds for Image-GS at comparable quality.
Outperforms Image-GS and Instant-NGP across standard image benchmarks when bitrate is held constant.

Where Pith is reading between the lines

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

The anisotropic metric per site could capture directional features such as edges or textures more efficiently than isotropic alternatives, potentially extending the same site-based representation to video or light-field data.
Because the representation remains fully explicit and differentiable, it may serve as a drop-in module inside larger neural pipelines that currently rely on implicit or grid-based encodings.
The jump-flooding top-K update combined with stochastic injection offers a general template for maintaining approximate nearest-neighbor structures in other domains where exact Voronoi computation is prohibitive.
Adaptive densification and pruning during training suggest a path toward automatic complexity control in other explicit scene representations that must balance fidelity against storage.

Load-bearing premise

The fixed-size per-pixel top-K approximation together with jump-flooding propagation and stochastic injection covers the image plane well enough to preserve fidelity under the anisotropic distance without noticeable artifacts or gradient bias.

What would settle it

Compare SAD reconstructions against an exact (non-approximated) anisotropic nearest-neighbor computation on the same sites; visible boundary artifacts or PSNR drop when top-K size is held constant would falsify the approximation claim.

Figures

Figures reproduced from arXiv: 2604.21984 by Laki Iinbor, Wojciech Matusik, Zhiyang Dou.

**Figure 1.** Figure 1: SAD achieves superior reconstruction quality and remarkably higher training speed across different compression rates and resolutions. At 2.0 BPP [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** Figure 2: Voronoi, power (Laguerre), and additively weighted Voronoi (Apollo [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: The Pipeline of SAD. Left: Given an input image, we initialize sites using content-adaptive sampling that places more sites in high-gradient regions (edges and textures). Middle: We jointly optimize site parameters including positions, colors, radii, and blending temperatures (𝜏). The Voronoi Partition row (bottom right) shows the evolving spatial decomposition, while the Tau Heatmap (top right) visualizes… view at source ↗

**Figure 4.** Figure 4: Representation diagram of our soft anisotropic additively weighted rendering. (1) Sites induce an anisotropic additively weighted diagram under the score𝑑mix (𝑥, 𝑖) = 𝑠 ∥𝑥−𝑝𝑖 ∥𝐺𝑖 −𝑠 𝑟𝑖 . Here 𝑝𝑖 sets position, 𝑟𝑖 controls reach, and 𝐺𝑖 controls orientation and anisotropic stretch. (2) For a query pixel 𝑥, we consider a small set of nearest candidate sites C (𝑥 ) under this score. (3) We compute temperature… view at source ↗

**Figure 5.** Figure 5: Top-𝐾 propagation algorithm for maintaining per-pixel candidate site sets at constant cost. (1) Initialize each pixel’s list with the previous top-𝐾 set C𝑡−1 (𝑥 ) (temporal reuse). (2) Spatial propagation: merge candidate site IDs from a fixed neighborhood (self + 4 neighbors) using the current jump step 𝑠𝑡 . (3) After propagation, each pixel holds an expanded candidate pool. (4) A small global probe step… view at source ↗

**Figure 6.** Figure 6: Threadgroup hash table gradient accumulation. (1) Each tile processes multiple pixels, with each pixel potentially affected by multiple sites (shown in different colors). (2) Sites are hashed into a threadgroup-local hash table where gradients are accumulated using local atomics. When sites collide (e.g., 𝑠3 and 𝑠4 both hash to slot 2), open addressing is used with bounded probing. (3) After all pixels in … view at source ↗

**Figure 7.** Figure 7: Qualitative comparison on DIV2K. Results for Instant-NGP, Image-GS, and SAD; error maps are shown at the bottom-right of each result. Critically, SAD not only runs faster per epoch but also attains higher final quality under the official step budgets (Image-GS 5,000, Instant-NGP 10,000, ours 4,000). As shown in our convergence analysis (Section 6.4), SAD achieves strong reconstruction quality (37.5 dB PSN… view at source ↗

**Figure 8.** Figure 8: Training performance: time per epoch vs image resolution. We report time per epoch (one full pass over all pixels) across methods. All methods were trained at 1.0 BPP on five test resolutions (5122 to 20482 ) with three runs each. For Instant-NGP, we set batch size equal to total pixels to ensure each step processes exactly one epoch; standard NGP uses a fixed 262k batch size, resulting in vastly different… view at source ↗

**Figure 9.** Figure 9: Convergence analysis. Average PSNR vs training time across three resolution/bitrate configurations. All show similar convergence patterns: quality plateaus around half the maximum training time (2000 iterations), with minimal improvement or slight degradation from longer training. Domain, Sites 8 passes 12 passes 16 passes 10242 16k 0.963 0.970 0.970 65k 0.398 0.867 0.867 131k 0.072 0.782 0.782 20482 16k 0… view at source ↗

**Figure 10.** Figure 10: Effect of site budget on reconstruction quality. Three 2048×1900 DIY photos rendered by SAD at 3k/6k/12k/24k sites (left to right), with the original in the final column. prune removes the lowest removal-delta sites; the prune/densify percentiles are automatically rescaled to meet the target count under the fixed iteration budget. 6.8 Ablation Study on Learnable Parameters We conduct a comprehensive ablat… view at source ↗

**Figure 11.** Figure 11: Effect of learnable parameters on cell structure and reconstruction. Top row: SAD diagrams. Bottom row: Reconstructed images. From left to right: Fixed log𝜏 = 7.5, Adaptive Tau, +Radius, +Anisotropy, Full model (+Radius+Anisotropy). Anisotropic cells create characteristic spiral patterns in smooth regions and align with edges in detailed areas [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗

**Figure 12.** Figure 12: Effect of fixed temperature on reconstruction. From left to right: log𝜏 = 10.0 (23.96 dB), log𝜏 = 7.5 (25.12 dB), log𝜏 = 5.0 (25.37 dB). Higher temperatures produce sharper boundaries while lower temperatures create softer blending. 7 More Applications 7.1 Differentiable PDE Solving Beyond image fitting, SAD serves as an adaptive mesh-free representation for differentiable physics simulation. We demonstr… view at source ↗

**Figure 13.** Figure 13: Differentiable Poisson solving on irregular domain. Top: Ground truth solution, shaded heightfield visualization, and binary mask defining the smiley domain. Bottom: Our reconstructed solution, shaded output, and learned site IDs. The colorful ID map reveals adaptive site concentration near boundaries and high-curvature features. Explicit sites enable hard constraint enforcement by freezing boundary site… view at source ↗

**Figure 14.** Figure 14: 1D signal fitting at a matched 256-parameter budget. Rows: SAD (64 sites × 4 params), Gaussian splatting [Kerbl et al. 2023] (64 splats × 4 params), and SIREN [Sitzmann et al. 2020] ([1, 16, 16, 1],𝜔0=15, 321 params). Columns: smooth sine, step-plus-sine, and multi-frequency periodic target. Dots on the SAD and Gaussian rows mark primitive positions. Gaussian splatting fits smooth regions near-optimally b… view at source ↗

read the original abstract

We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted distance score, and we compute pixel colors as a softmax blend over a small per-pixel top-K subset of sites. We induce a soft anisotropic additively weighted Voronoi partition (i.e., an Apollonius diagram) with learnable per-site temperatures, preserving informative gradients while allowing clear, content-aligned boundaries and explicit ownership. Such a formulation enables efficient rendering by maintaining a per-query top-K map that approximates nearest neighbors under the same shading score, allowing GPU-friendly, fixed-size local computation. We update this list using our top-K propagation scheme inspired by jump flooding, augmented with stochastic injection to provide probabilistic global coverage. Training follows a GPU-first pipeline with gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. Across standard benchmarks, SAD consistently outperforms Image-GS and Instant-NGP at matched bitrate. On Kodak, SAD reaches 46.0 dB PSNR with 2.2 s encoding time (vs. 28 s for Image-GS), and delivers 4-19 times end-to-end training speedups over state-of-the-art baselines. We demonstrate the effectiveness of SAD by showcasing the seamless integration with differentiable pipelines for forward and inverse problems, efficiency of fast random access, and compact storage.

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.

Desk Editor's Note private letter to a colleague

SAD gives a workable explicit differentiable image rep via soft anisotropic Apollonius diagrams with top-K approximation, but the performance numbers depend on an approximation whose coverage under anisotropy is not yet clearly bounded.

read the letter

The paper's main advance is a formulation for soft anisotropic additively weighted diagrams (Apollonius style) where each site carries its own anisotropic metric and temperature, and pixel values come from a softmax over a small top-K set of sites. The top-K map is maintained with jump-flooding propagation plus stochastic injection so that the whole thing stays GPU-friendly and differentiable. That combination of anisotropy, additive weights, learnable temperatures, and the specific propagation trick is not in the baselines they cite, so the construction itself is new. They show it can be trained end-to-end with Adam, densification/pruning, and gradient-weighted init, and they report concrete speed and quality numbers: 46 dB PSNR on Kodak in 2.2 s encoding versus 28 s for Image-GS, plus 4-19x training speedups at matched bitrate. The integration claims with forward and inverse differentiable pipelines are also useful to see in practice. The soft spot is exactly the one the stress-test flags. Because the distance is both anisotropic and additively weighted, site ordering can change sharply across the plane. A fixed-K local stencil propagated from jump-flooding (originally Euclidean) plus occasional random injections may miss high-weight sites or keep irrelevant ones, so the softmax blend deviates from the true soft partition. The abstract gives no quantitative bound on the approximation error, no ablation that turns off the stochastic injection, and no check for gradient bias or visible artifacts. If those checks are in the full paper and the error stays small, the outperformance claims hold; if not, the PSNR numbers could be partly fitting artifacts. The experimental protocol details are also thin in the summary, so it is hard to judge how general the gains are beyond the reported datasets. This work is aimed at people who need compact, explicit, and fast-to-optimize image or scene representations inside ML pipelines. A reader already working on differentiable rendering or explicit neural fields would get the most out of the formulation and the speed numbers. It is worth sending to peer review because the core idea is fresh and the efficiency results, if they survive scrutiny on the approximation, would be practically relevant. Ask the authors for the missing ablations and error analysis on the top-K scheme before acceptance.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Soft Anisotropic Diagrams (SAD), an explicit differentiable image representation using a set of adaptive sites in the image plane. Each site defines an anisotropic metric and additively weighted distance; pixel colors are obtained as a softmax blend over a small per-pixel top-K subset of sites, inducing a soft anisotropic additively weighted Voronoi partition (Apollonius diagram) with learnable per-site temperatures. The top-K map is updated via a jump-flooding-inspired propagation scheme augmented with stochastic injection. Training uses gradient-weighted initialization, Adam, and adaptive densification/pruning. The paper claims consistent outperformance over Image-GS and Instant-NGP at matched bitrate, with specific results such as 46.0 dB PSNR on Kodak at 2.2 s encoding time and 4-19x end-to-end speedups.

Significance. If the top-K approximation is shown to be faithful, SAD would offer a compact, explicit, and GPU-efficient differentiable representation that supports fast random access and seamless integration into forward/inverse differentiable pipelines, providing measurable gains in both fidelity and training speed over current explicit and implicit baselines.

major comments (2)

[Description of the top-K propagation scheme and stochastic injection] The headline quantitative claims (e.g., 46.0 dB PSNR and speedups) rest on the assertion that the fixed-size per-pixel top-K map, maintained by jump-flooding propagation plus stochastic injection, yields a faithful approximation to the true soft anisotropic additively weighted diagram. No quantitative bound on approximation error, coverage analysis, or ablation that isolates/removes the stochastic injection is supplied, leaving open the risk of omitted high-weight sites or gradient bias under the anisotropic distance.
[Experimental results and benchmarks] The experimental section reports strong PSNR and timing numbers against baselines but provides no detailed protocol, error bars, ablation of the top-K approximation, or verification that the reported PSNR reflects true image fidelity rather than artifacts induced by the local stencil.

minor comments (2)

[Formulation of SAD] Clarify the precise mathematical definition of the anisotropic metric and the additively weighted distance score used in the softmax blend.
[Training pipeline] Specify the exact criteria and thresholds used for densification and pruning in the adaptive budget control.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below, providing clarifications and committing to specific revisions that strengthen the manuscript without altering its core claims.

read point-by-point responses

Referee: The headline quantitative claims (e.g., 46.0 dB PSNR and speedups) rest on the assertion that the fixed-size per-pixel top-K map, maintained by jump-flooding propagation plus stochastic injection, yields a faithful approximation to the true soft anisotropic additively weighted diagram. No quantitative bound on approximation error, coverage analysis, or ablation that isolates/removes the stochastic injection is supplied, leaving open the risk of omitted high-weight sites or gradient bias under the anisotropic distance.

Authors: We acknowledge that the current manuscript lacks a formal quantitative bound on the top-K approximation error and does not include an explicit ablation isolating stochastic injection. The jump-flooding scheme propagates high-weight sites locally while stochastic injection ensures probabilistic global coverage; empirical results (higher PSNR than baselines) indicate the approximation is effective in practice. In the revision we will add: (i) a coverage analysis reporting the fraction of pixels where the maintained top-K differs from the true top-K under the full anisotropic distance, (ii) an ablation removing stochastic injection to quantify its contribution to PSNR and stability, and (iii) a brief discussion of gradient flow through the softmax, which remains non-zero for all sites retained in the top-K. These additions will directly address the risk of omitted sites or bias. revision: yes
Referee: The experimental section reports strong PSNR and timing numbers against baselines but provides no detailed protocol, error bars, ablation of the top-K approximation, or verification that the reported PSNR reflects true image fidelity rather than artifacts induced by the local stencil.

Authors: We agree that the experimental section would benefit from greater detail and additional validation. In the revised manuscript we will expand the protocol description to include all hyperparameters, initialization details, and hardware specifications; report error bars from at least three independent runs for the primary Kodak and other benchmark results; add a dedicated ablation on top-K size and propagation parameters; and include SSIM and LPIPS metrics together with side-by-side visual comparisons. These supplementary metrics and visuals will confirm that the reported PSNR improvements correspond to genuine fidelity gains rather than stencil-induced artifacts, as the learned boundaries already align with image content in the current figures. revision: yes

Circularity Check

0 steps flagged

No circularity detected; SAD is a novel explicit construction evaluated empirically

full rationale

The paper defines SAD directly via adaptive sites, per-site anisotropic metrics, additively weighted distances, and a softmax blend over a fixed-size top-K map updated by jump-flooding plus stochastic injection. This construction is presented as an engineering approximation to the soft Apollonius diagram without any step that reduces by definition to its own fitted outputs or renames an input as a prediction. No load-bearing self-citations appear in the provided text, and performance numbers (e.g., 46.0 dB PSNR on Kodak) are reported as direct empirical comparisons against external baselines rather than derived quantities. The derivation chain therefore remains self-contained and independent of the target results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the method builds on standard Voronoi and softmax concepts from prior literature.

pith-pipeline@v0.9.0 · 5561 in / 1203 out tokens · 47322 ms · 2026-05-09T21:41:20.963717+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

87 extracted references · 14 canonical work pages

[1]

ACM SIGGRAPH 2024 Conference Papers , pages=

Gem3d: Generative medial abstractions for 3d shape synthesis , author=. ACM SIGGRAPH 2024 Conference Papers , pages=

2024
[2]

The Computational Geometry Algorithms Library , author =
[3]

Menelaos Karavelas , subtitle =
[4]

The Computational Geometry Algorithms Library , subtitle =

Menelaos Karavelas , editor =. The Computational Geometry Algorithms Library , subtitle =
[5]

The Parmap library , author =
[6]

Christopher Anderson and Sophia Drossopoulou , title =
[7]

SIAM journal on computing , volume=

Power diagrams: properties, algorithms and applications , author=. SIAM journal on computing , volume=. 1987 , publisher=

1987
[8]

ACM computing surveys (CSUR) , volume=

Voronoi diagrams—a survey of a fundamental geometric data structure , author=. ACM computing surveys (CSUR) , volume=. 1991 , publisher=

1991
[9]

Nouvelles applications des param

Voronoi, Georges , journal=. Nouvelles applications des param. 1908 , publisher=

1908
[10]

Japanese Conference on Discrete and Computational Geometry , pages=

An interpolant based on line segment Voronoi diagrams , author=. Japanese Conference on Discrete and Computational Geometry , pages=. 1998 , organization=

1998
[11]

Proceedings of the eleventh annual symposium on Computational geometry , pages=

Voronoi diagrams in higher dimensions under certain polyhedral distance functions , author=. Proceedings of the eleventh annual symposium on Computational geometry , pages=
[12]

Proceedings of the 27th annual conference on Computer graphics and interactive techniques , pages=

Surfels: Surface elements as rendering primitives , author=. Proceedings of the 27th annual conference on Computer graphics and interactive techniques , pages=
[13]

Lossy image compres- sion with compressive autoencoders,

Lossy image compression with compressive autoencoders , author=. arXiv preprint arXiv:1703.00395 , year=

work page arXiv
[14]

Acorn: Adaptive coordinate networks for neural scene representation.arXiv preprint arXiv:2105.02788, 2021

Acorn: Adaptive coordinate networks for neural scene representation , author=. arXiv preprint arXiv:2105.02788 , year=

work page arXiv
[15]

arXiv preprint arXiv:2305.17105 , year=

Random-access neural compression of material textures , author=. arXiv preprint arXiv:2305.17105 , year=

work page arXiv
[16]

Proceedings of the fourteenth annual symposium on Computational geometry , pages=

Surface reconstruction by Voronoi filtering , author=. Proceedings of the fourteenth annual symposium on Computational geometry , pages=
[17]

Proceedings of the 25th annual conference on Computer graphics and interactive techniques , pages=

A new Voronoi-based surface reconstruction algorithm , author=. Proceedings of the 25th annual conference on Computer graphics and interactive techniques , pages=
[18]

ACM Transactions on Graphics (TOG) , volume=

Medial Skeletal Diagram: A Generalized Medial Axis Approach for Compact 3D Shape Representation , author=. ACM Transactions on Graphics (TOG) , volume=. 2024 , publisher=

2024
[19]

arXiv preprint arXiv:2403.18761 , year=

MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram , author=. arXiv preprint arXiv:2403.18761 , year=

work page arXiv
[20]

ACM Transactions on Graphics (TOG) , volume=

Computing medial axis transform with feature preservation via restricted power diagram , author=. ACM Transactions on Graphics (TOG) , volume=. 2022 , publisher=

2022
[21]

ACM Transactions on Graphics (TOG) , volume=

Globally consistent normal orientation for point clouds by regularizing the winding-number field , author=. ACM Transactions on Graphics (TOG) , volume=. 2023 , publisher=

2023
[22]

Advances in Neural Information Processing Systems , volume=

Tetrahedron splatting for 3d generation , author=. Advances in Neural Information Processing Systems , volume=
[23]

Computer Graphics Forum , volume=

Pinchmaps: Textures with customizable discontinuities , author=. Computer Graphics Forum , volume=
[24]

ACM Transactions on Graphics (TOG) , volume=

Real-time rendering of textures with feature curves , author=. ACM Transactions on Graphics (TOG) , volume=. 2008 , publisher=

2008
[25]

Radiant foam: Real-time differen- tiable ray tracing.arXiv:2502.01157, 2025

Radiant foam: Real-time differentiable ray tracing , author=. arXiv preprint arXiv:2502.01157 , year=

work page arXiv
[26]

, author=

Bixels: Picture Samples with Sharp Embedded Boundaries. , author=. Rendering Techniques , volume=
[27]

Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , pages=

Scale-dependent reproduction of pen-and-ink illustrations , author=. Proceedings of the 23rd annual conference on Computer graphics and interactive techniques , pages=
[28]

2004 , institution=

Feature-based textures , author=. 2004 , institution=

2004
[29]

Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

Learned image compression with discretized gaussian mixture likelihoods and attention modules , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=
[30]

ACM SIGGRAPH 2022 conference proceedings , pages=

Relu fields: The little non-linearity that could , author=. ACM SIGGRAPH 2022 conference proceedings , pages=

2022
[31]

Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

Cool-chic: Coordinate-based low complexity hierarchical image codec , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=
[32]

arXiv preprint arXiv:2201.12904 , year=

Coin++: Neural compression across modalities , author=. arXiv preprint arXiv:2201.12904 , year=

work page arXiv
[33]

End-to-end optimized image compression.arXiv preprint arXiv:1611.01704, 2016

End-to-end optimized image compression , author=. arXiv preprint arXiv:1611.01704 , year=

work page arXiv
[34]

, author=

3D Gaussian splatting for real-time radiance field rendering. , author=. ACM Trans. Graph. , volume=
[35]

ACM SIGGRAPH 2024 conference papers , pages=

2d gaussian splatting for geometrically accurate radiance fields , author=. ACM SIGGRAPH 2024 conference papers , pages=

2024
[36]

Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, 2005

High-quality surface splatting on today's GPUs , author=. Proceedings Eurographics/IEEE VGTC Symposium Point-Based Graphics, 2005. , pages=. 2005 , organization=

2005
[37]

Proceedings of the 28th annual conference on Computer graphics and interactive techniques , pages=

Surface splatting , author=. Proceedings of the 28th annual conference on Computer graphics and interactive techniques , pages=
[38]

11th Pacific Conference onComputer Graphics and Applications, 2003

High-quality point-based rendering on modern GPUs , author=. 11th Pacific Conference onComputer Graphics and Applications, 2003. Proceedings. , pages=. 2003 , organization=

2003
[39]

Computational Geometry , volume=

The predicates of the Apollonius diagram: algorithmic analysis and implementation , author=. Computational Geometry , volume=. 2006 , publisher=

2006
[40]

Proceedings of the IEEE/CVF international conference on computer vision , pages=

Soft rasterizer: A differentiable renderer for image-based 3d reasoning , author=. Proceedings of the IEEE/CVF international conference on computer vision , pages=
[41]

ACM SIGGRAPH 2025 Conference Proceedings , year=

Image-GS: Content-Adaptive Image Representation via 2D Gaussians , author=. ACM SIGGRAPH 2025 Conference Proceedings , year=

2025
[42]

European Conference on Computer Vision (ECCV) , year=

GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting , author=. European Conference on Computer Vision (ECCV) , year=
[43]

Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

Instant GaussianImage: A Generalizable and Self-Adaptive Image Representation via 2D Gaussian Splatting , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=
[44]

Advances in Neural Information Processing Systems (NeurIPS) , year=

Implicit Neural Representations with Periodic Activation Functions , author=. Advances in Neural Information Processing Systems (NeurIPS) , year=
[45]

Advances in Neural Information Processing Systems (NeurIPS) , year=

Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains , author=. Advances in Neural Information Processing Systems (NeurIPS) , year=
[46]

Proceedings of the AAAI Conference on Artificial Intelligence , volume=

Large Images Are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting , author=. Proceedings of the AAAI Conference on Artificial Intelligence , volume=
[47]

arXiv preprint arXiv:2512.12774 , year=

Fast 2DGS: Efficient Image Representation with Deep Gaussian Prior , author=. arXiv preprint arXiv:2512.12774 , year=

work page arXiv
[48]

Proceedings of the IEEE conference on computer vision and pattern recognition , pages=

Deep image prior , author=. Proceedings of the IEEE conference on computer vision and pattern recognition , pages=
[49]

Advances in neural information processing systems , volume=

Implicit neural representations with periodic activation functions , author=. Advances in neural information processing systems , volume=
[50]

5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2024) , year=

SDF-PINNs: Joining Physics-Informed Neural Networks with Neural Implicit Geometry Representation , author=. 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2024) , year=

2024
[51]

ACM Transactions on Graphics (ToG) , volume=

Instant Neural Graphics Primitives with a Multiresolution Hash Encoding , author=. ACM Transactions on Graphics (ToG) , volume=. 2022 , publisher=

2022
[52]

Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops , pages=

NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study , author=. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops , pages=

2017
[53]

Challenge on Learned Image Compression , author=
[54]

Kodak Lossless True Color Image Suite , year =
[55]

, author=

Differentiable surface triangulation. , author=. ACM Trans. Graph. , volume=
[56]

ACM Transactions on Graphics (TOG) , volume=

Vector regression functions for texture compression , author=. ACM Transactions on Graphics (TOG) , volume=. 2015 , publisher=

2015
[57]

arXiv preprint arXiv:2512.14180 (2025) 2, 10, 11

Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere , author=. arXiv preprint arXiv:2512.14180 , year=

work page arXiv
[58]

SIAM Review , volume=

Centroidal Voronoi tessellations: Applications and algorithms , author=. SIAM Review , volume=. 1999 , publisher=

1999
[59]

2nd International Symposium on Non-Photorealistic Animation and Rendering (NPAR 2002) , pages=

Weighted Voronoi stippling , author=. 2nd International Symposium on Non-Photorealistic Animation and Rendering (NPAR 2002) , pages=. 2002 , organization=

2002
[60]

Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics , pages=

Some methods for classification and analysis of multivariate observations , author=. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics , pages=. 1967 , organization=

1967
[61]

Proceedings of the 2006 symposium on Interactive 3D graphics and games , pages=

Jump flooding in GPU with applications to Voronoi diagram and distance transform , author=. Proceedings of the 2006 symposium on Interactive 3D graphics and games , pages=

2006
[62]

SIGGRAPH Asia 2023 Conference Papers (SA 2023) , pages=

Efficient Graphics Representation with Differentiable Indirection , author=. SIGGRAPH Asia 2023 Conference Papers (SA 2023) , pages=. 2023 , organization=

2023
[63]

Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops , pages=

Voronoinet: General functional approximators with local support , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops , pages=
[64]

Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

Voromesh: Learning watertight surface meshes with voronoi diagrams , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=
[65]

International Journal for Numerical Methods in Engineering , volume=

Cellular topology optimization on differentiable Voronoi diagrams , author=. International Journal for Numerical Methods in Engineering , volume=. 2023 , publisher=

2023
[66]

Pacific Graphics Conference Papers and Posters , volume=

Free-form floor plan design using differentiable Voronoi diagram , author=. Pacific Graphics Conference Papers and Posters , volume=
[67]

arXiv preprint arXiv:2512.12984 , year=

VoroLight: Learning Quality Volumetric Voronoi Meshes from General Inputs , author=. arXiv preprint arXiv:2512.12984 , year=

work page arXiv
[68]

ACM Transactions on Graphics (TOG) , volume=

Q-mat: Computing medial axis transform by quadratic error minimization , author=. ACM Transactions on Graphics (TOG) , volume=. 2015 , publisher=

2015
[69]

4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) , pages=

Voronoi diagram in optimal path planning , author=. 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) , pages=. 2007 , organization=

2007
[70]

IEEE Transactions on robotics and automation , volume=

Motion planning in a plane using generalized Voronoi diagrams , author=. IEEE Transactions on robotics and automation , volume=. 1989 , publisher=

1989
[71]

Computer-Aided Design , volume=

Surface reconstruction by computing restricted voronoi cells in parallel , author=. Computer-Aided Design , volume=. 2017 , publisher=

2017
[72]

Computer Graphics Forum , volume=

Coverage axis++: Efficient inner point selection for 3D shape skeletonization , author=. Computer Graphics Forum , volume=. 2024 , organization=

2024
[73]

Computer Graphics Forum , volume=

Coverage axis: Inner point selection for 3d shape skeletonization , author=. Computer Graphics Forum , volume=. 2022 , organization=

2022
[74]

Proceedings of the sixth ACM symposium on Solid modeling and applications , pages=

The power crust , author=. Proceedings of the sixth ACM symposium on Solid modeling and applications , pages=
[75]

Computer-Aided Design , volume=

Efficient computation of clipped Voronoi diagram for mesh generation , author=. Computer-Aided Design , volume=. 2013 , publisher=

2013
[76]

Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

Wire: Wavelet implicit neural representations , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=
[77]

Coin: Compression with implicit neural representations.arXiv preprint arXiv:2103.03123, 2021

Coin: Compression with implicit neural representations , author=. arXiv preprint arXiv:2103.03123 , year=

work page arXiv
[78]

Advances in neural information processing systems , volume=

Fourier features let networks learn high frequency functions in low dimensional domains , author=. Advances in neural information processing systems , volume=
[79]

Acta Numerica , volume=

Radial basis functions , author=. Acta Numerica , volume=. 2000 , publisher=

2000
[80]

1978 , publisher=

A Practical Guide to Splines , author=. 1978 , publisher=

1978

Showing first 80 references.