3D Gaussian Splatting for Real-Time Radiance Field Rendering
ACM Transactions on Graphics, 2023 · paper · Computer science
Represents scenes with optimized 3D Gaussians and a fast visibility-aware renderer for novel-view synthesis. The authors report state-of-the-art visual quality, training times competitive with the fastest methods, and real-time (at least 30 fps) 1080p rendering.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
7 findings
Reference or label Sec. 7.2: "the current state-of-the-art is Mip-Nerf360 [Barron et al. 2021]"; the 2021 entry in the reference list is "Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields", and Mip-NeRF 360 is the Barron et al. 2022 entry cited everywhere else.
- p. 8 Sec. 7.2, Real-World Scenes
art is Mip-Nerf360 [Barron et al. 2021]
- p. 12 References
2021. Mip-nerf: A multiscale representation for
- p. 8 Section 7.2, Results
proach on the full set of scenes presented in Mip-Nerf360 [Barron
- p. 8 Sec. 7.2 Real-World Scenes
Mip-Nerf360 [Barron et al. 2021]
Judge's note: Checked page 8 and the reference list on page 12. The reference list has two Barron entries: 2021 (Mip-NeRF, ICCV) and 2022 (Mip-NeRF 360, CVPR). The sentence names Mip-NeRF360 as the quality benchmark, and the paragraph just above on the same page, the Fig. 1 caption and Sec. 1 all cite it as Barron et al. 2022. The citation year here points to the wrong entry. Settled from the paper's own reference list; no outside fact needed. The spelling "Mip-Nerf360" also differs from "Mip-NeRF360" used elsewhere.
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Reference or label Sec. 7.4 figure pointers appear exchanged: "In regions where the scene is not well observed we have artifacts ... (e.g., Mip-NeRF360 in Fig. 11)" and "elongated artifacts or “splotchy” Gaussians (see Fig. 12)", whereas Fig. 11 shows "coarse, anisoptropic Gaussians" and Fig. 12 shows "views that have little overlap with those seen during training".
- p. 11 Fig. 11 caption
anisoptropic Gaussians resulting in low-detail visuals
- p. 10 Section 7.4, first paragraph
ods also struggle (e.g., Mip-NeRF360 in Fig. 11)
- p. 10 Section 7.4, first paragraph
(see Fig. 12); again previous methods also struggle in these cases.
- p. 11 Fig. 11 caption
anisoptropic Gaussians resulting in low-detail visuals (right, background).
Only the authors can say what is right here.
Judge's note: Page 10 image (Sec. 7.4) and page 11 image (captions of Figs. 11 and 12) read as quoted. The poorly-observed-region sentence points to Fig. 11, whose caption describes coarse anisotropic Gaussians (the elongated/splotchy failure); the splotchy-Gaussians sentence points to Fig. 12, whose caption describes views with little overlap with training views (the poorly observed case). Each caption fits the other sentence. Both figures do show a Mip-NeRF360 comparison, so the authors should confirm, hence author_query. This cluster also carries the "anisoptropic" misspelling in the Fig. 11 caption, which is real and is recorded under C026.
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Wording Sec. 1 says the optimisation gives "(1-5 million Gaussians for all scenes tested)", but Sec. 7.2 reports that for the synthetic Blender scenes the trained model "reaches about 200–500K Gaussians per scene".
- p. 2 Sec. 1, second component
million Gaussians for all scenes tested
- p. 9 Sec. 7.2, Synthetic Bounded Scenes
iterations reaches about 200–500K Gaussians per scene
- p. 2 Section 1, third paragraph
(1-5 million Gaussians for all scenes tested)
- p. 9 Section 7.2, Synthetic Bounded Scenes
reaches about 200–500K Gaussians per scene
Only the authors can say what is right here.
Judge's note: Read page 2 and page 9. The synthetic Blender scenes are part of the evaluation (Sec. 7.2 Results, Table 2), and the same introduction paragraph mentions the NeRF-synthetic dataset, so they are among the scenes tested. 200-500K is below the stated lower bound of 1 million. I found no qualifier limiting the introduction's range to the real scenes. The likely intent is the 13 real scenes, so this is an overgeneralised wording, not a wrong measurement.
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Wording The definition after Eq. 2 prints the transmittance as a product over j = 1..i−1 of "(1 − α_i)"; the factor should be (1 − α_j), as in Eq. 3 and as implied by the sum over σ_j δ_j in Eq. 1.
- p. 3 Sec. 2.3, definition following Eq. 2
(1 − 𝛼𝑖)
- p. 3 Sec. 2.3, Eq. 3
(1 − 𝛼𝑗)
- p. 3 Eq. 2 definitions
𝑇𝑖= 𝑖−1 Ö 𝑗=1 (1 −𝛼𝑖)
Judge's note: Checked on the page 3 image: the product index is j and the factor's subscript is i, while Eq. 3 directly below has (1 − α_j). As printed the product does not depend on its index. From Eq. 1, T_i = exp(−Σ_{j<i} σ_j δ_j) = Π_{j<i}(1 − α_j). This is an index slip in an equation with an evident fix; the surrounding argument (Eq. 2 and Eq. 3 are the same model) relies on the corrected form.
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Wording Sec. 2.2: "Both rely on Spherical Harmonics: the former to represent directional effects directly, the latter to encode its inputs to the color network"; "former" is InstantNGP (described as using an MLP) and "latter" is Plenoxels (described as able "to forgo neural networks altogether"), so the two roles are reversed.
- p. 3 Sec. 2.2, paragraph on InstantNGP and Plenoxels
the former to represent directional effects directly, the latter to encode its inputs to the color network
- p. 3 Sec. 2.2, preceding sentence
are able to forgo neural networks altogether
- p. 3 Section 2.2, paragraph beginning "Most notable of these methods"
former to represent directional effects directly, the latter to encode
- p. 3 Section 2.2, same paragraph
grid to interpolate a continuous density field, and are able to forgo
Judge's note: Read the paragraph on page 3. InstantNGP is named first, with "a smaller MLP to represent density and appearance"; Plenoxels is named second and is said to forgo neural networks. The next sentence gives the colour network to the latter (Plenoxels) and direct spherical-harmonic representation to the former (InstantNGP). That contradicts the preceding sentence on the same page, so the swap is established from the paper itself without outside knowledge.
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Wording "note that on the same hardware, their average training time was 48 hours" is contradicted by its own footnote: "We trained Mip-NeRF360 on a 4-GPU A100 node for 12 hours, equivalent to 48 hours on a single GPU. Note that A100’s are faster than A6000 GPUs."
- p. 9 Sec. 7.2, paragraph starting "The table shows"
note that on the same hardware, their aver-
- p. 9 Footnote 2
We trained Mip-NeRF360 on a 4-GPU A100 node for 12 hours
- p. 8 Sec. 7.2, Results
except for the Mip-NeRF360 method (see below)
- p. 9 Footnote 2
We trained Mip-NeRF360 on a 4-GPU A100 node for 12 hours, equivalent to 48 hours
Only the authors can say what is right here.
Judge's note: Page 9 image: the sentence says "on the same hardware" and carries footnote 2, which states the training ran on a 4-GPU A100 node and that A100s are faster than A6000s. Page 8 says all results run on an A6000 "except for the Mip-NeRF360 method (see below)". So the 48 h is a GPU-hour conversion on different hardware, not a measurement on the same hardware. The paper discloses the real setup in the footnote and the exception on page 8, so the reader is not left with a wrong number, but the phrase "on the same hardware" is wrong as worded for the training time (it may have been meant for the rendering speed only). Rated as wording.
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Wording Algorithm 2's first step is "CullGaussian(𝑝, 𝑉)", but 𝑝 is not among the declared inputs (𝑤, ℎ, 𝑀, 𝑆, 𝐶, 𝐴, 𝑉) and is not defined anywhere in the algorithm; Gaussian means are 𝑀.
- p. 14 Algorithm 2, first line of function body
CullGaussian(𝑝, 𝑉)
Only the authors can say what is right here.
Judge's note: Checked the Algorithm 2 crop and page 14: the header lists w, h, M, S, C, A, V, with 'M, S: Gaussian means and covariances in world space'. The culling call uses p, and the very next line uses M, S, V. Algorithm 1 on page 13 also names positions M (with μ for a single Gaussian) and uses p only as a subscript (∇_p L, τ_p). So p is an undefined symbol here, most likely meaning the positions M; the authors would need to confirm the intended argument.
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21 minor (typos and the like; most checked by the judge only)
Wording Fig. 1 labels the InstantNGP bicycle panel "Train: 7min, PSNR: 22.1", while Table 5 gives bicycle PSNR 22.193 (INGP-Base) and 22.171 (INGP-Big), both of which round to 22.2.
- p. 1 Fig. 1, InstantNGP panel
Train: 7min, PSNR: 22.1
- p. 14 Table 5, bicycle column, INGP-Base and INGP-Big
22.171
Judge's note: Checked the Fig. 1 crop and Table 5 on page 14. The other four panels match the bicycle column after rounding (21.912 to 21.9, 24.305 to 24.3, 23.604 to 23.6, 25.246 to 25.2). The InstantNGP label is 0.1 lower than either configuration rounds to; it matches only if truncated. No statement in the paper says Fig. 1 uses a different run or a single view. The difference is under 0.1 dB and changes no conclusion, so it is a minor consistency point.
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Wording "compared to our 35-45min" does not cover the Table 1 Ours-30K training time for Tanks&Temples ("26m54s"); the other two datasets (41m33s, 36m2s) fall inside the range.
- p. 9 Sec. 7.2, paragraph starting "The table shows"
compared to our 35-45min
- p. 8 Table 1, Ours-30K, Tanks&Temples Train
26m54s
- p. 1 Fig. 1, right-hand Ours panel
Train: 51min, PSNR: 25.2
Judge's note: Page 9 image: the sentence refers to "The table" (Table 1) and compares against Mip-NeRF360's 48 h, which Table 1 lists for all three datasets. Page 8 image, Table 1 Ours-30K Train column: 41m33s, 26m54s, 36m2s. The Tanks&Temples average is about 8 minutes below the stated lower bound. No statement restricts the range to two datasets; the preceding paragraph only says times vary over datasets and are reported separately. Fig. 1's 51 min (page 1) is a single scene (bicycle), a different quantity from dataset averages, so that part is not counted. A loose summary range rather than a wrong result.
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Wording The text says the Gaussian is "centered at point (mean) μ", but Eq. 4 is printed as G(x) = e^{−½ (x)^T Σ^{−1} (x)} with no μ.
- p. 4 Sec. 4, sentence before Eq. 4 and Eq. 4
centered at point (mean) 𝜇
- p. 4 Eq. 4
𝐺(𝑥) = 𝑒−1 2 (𝑥)𝑇Σ−1(𝑥)
Judge's note: Checked the crop and page 4. Eq. 4 as printed is a Gaussian centred at the origin; μ is introduced in the sentence immediately before and does not appear in the equation, and the paper does not say x is measured relative to the mean. Either (x − μ) is missing or that convention should be stated. The intended meaning is clear, so this is a minor notation gap.
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Wording Sec. 6: "Specifically, each point stores the final accumulated opacity α in the forward process"; the accumulated opacity at the end of blending is a per-pixel quantity, and the section earlier claims "only a constant overhead per pixel".
- p. 6 Sec. 6, last paragraph
point stores the final accumulated opacity 𝛼 in the forward process
- p. 6 Sec. 6, second paragraph
requiring only a constant overhead per pixel
Only the authors can say what is right here.
Judge's note: Read Sec. 6 on page 6. The preceding sentence says only the total accumulated opacity at the end of the forward pass is stored, and the next clause divides it by "each point's α" during the per-pixel back-to-front traversal. Elsewhere in the section "point" means a Gaussian, and one Gaussian covers many pixels with different accumulated opacity, so per-point storage does not fit the constant-per-pixel claim. "Each pixel" appears to be meant, but the text does not settle it and only the authors can confirm.
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Wording Algorithm 1 calls "𝐼 ← Rasterize(𝑀, 𝑆, 𝐶, 𝐴, 𝑉)" with the comment "Alg. 2", but Algorithm 2 defines "function Rasterize(𝑤, ℎ, 𝑀, 𝑆, 𝐶, 𝐴, 𝑉)"; w and h are declared in Algorithm 1 but never used.
- p. 13 Algorithm 1
𝐼 ← Rasterize(𝑀, 𝑆, 𝐶, 𝐴, 𝑉)
- p. 14 Algorithm 2
function Rasterize(𝑤, ℎ, 𝑀, 𝑆, 𝐶, 𝐴, 𝑉)
Judge's note: Page 13 image (Algorithm 1) shows the five-argument call and the header "w, h: width and height of the training images"; page 14 image (Algorithm 2) shows the seven-parameter definition. The call omits w and h. Pseudocode shorthand whose meaning is recoverable, so a minor notational inconsistency.
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Wording Algorithm 2 iterates "for all Tiles 𝑡 in 𝐼 do" although the tile set is defined two lines earlier as "𝑇 ← CreateTiles(𝑤, ℎ)" and 𝐼 is the canvas just initialised to 0.
- p. 14 Algorithm 2, outer loop
for all Tiles 𝑡 in 𝐼 do
- p. 14 Algorithm 2
𝑇 ← CreateTiles(𝑤, ℎ)
Judge's note: Checked the Algorithm 2 crop and page 14. T is created by CreateTiles and used in DuplicateWithKeys and IdentifyTileRanges; the loop then ranges over I, the output image set by 'I ← 0'. Looping over T would be the consistent notation, but 'tiles t in (image) I' followed by 'pixels i in t' is also a readable hierarchy for a high-level overview, so this is a minor notational inconsistency and not a clear error.
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Typo Sec. 3: "Out fast rasterizer also includes" should read "Our fast rasterizer"; Fig. 11 caption: "anisoptropic Gaussians" should read "anisotropic".
- p. 4 Sec. 3, Overview
Out fast rasterizer also includes
- p. 4 Sec. 3 Overview
Out fast rasterizer
- p. 6 Sec. 6
trasversing
- p. 11 Fig. 11 caption
anisoptropic
Judge's note: Both misspellings are visible on the page images (page 4, Sec. 3 Overview; page 11, Fig. 11 caption). The third item in this cluster, "trasversing" on page 6, is also real and is handled as C013.
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Typo Threshold symbols differ between text and Algorithm 1: Sec. 5.2 has "a threshold τ_pos" and "a threshold ε_α", Algorithm 1 has "if ∇_p L > τ_p then" and "if α < ε or IsTooLarge(μ, Σ) then", and Appendix C uses plain ε for the blending skip threshold ("we choose ε as 1/255").
- p. 5 Sec. 5.2
gradients above a threshold 𝜏pos
- p. 13 Algorithm 1
if ∇𝑝𝐿 > 𝜏𝑝 then
- p. 13 Algorithm 1, pruning
if 𝛼 < 𝜖 or IsTooLarge(𝜇, Σ) then
- p. 14 Appendix C, Numerical stability
𝛼 < 𝜖 (we choose 𝜖 as
Judge's note: Checked page 5, Algorithm 1 on page 13 and Appendix C on page 14. The notation is inconsistent as described, and the paper does not say whether the plain ε of Appendix C is the same threshold as the pruning ε_α. Meaning can be inferred from context, so this is a minor notation point. The second reviewer note (a repeated "if") is not a defect: it is "end if" followed on the next line by "if" in the algorithm listing, an artefact of reading the lines as running text.
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Typo Sec. 6: "Rather than trasversing an explicit list" should read "traversing".
- p. 6 Sec. 6, last paragraph
Rather than trasversing an explicit
Judge's note: The misspelling is visible on the page 6 image; the same section uses "traverse" and "traversing" correctly elsewhere.
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Typo The same names are written in two ways: "DrJohnson" (Fig. 5 caption, Fig. 12 caption) versus "Dr Johnson" (Tables 7-9), and "Tanks&Temples" (Table 1, Fig. 5 caption, Tables 7-9) versus "For Tanks & Temples" (Sec. 7.2).
- p. 7 Fig. 5 caption
DrJohnson from the Deep Blending dataset
- p. 14 Table 7 header
Dr Johnson
- p. 9 Sec. 7.2
For Tanks & Temples
Judge's note: Checked the Fig. 5 caption crop, the Table 7-9 headers on page 14, Table 1 on page 8 and Sec. 7.2 on page 9. Both variants appear as described. This is a house-style inconsistency with no effect on meaning.
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Typo Citation printed without authors: "two scenes from the Tanks&Temples dataset [2017] and two scenes provided by Hedman et al. [Hedman et al. 2018]"; elsewhere the work is cited as [Knapitsch et al. 2017].
- p. 8 Sec. 7.2, Results
two scenes from the Tanks&Temples dataset [2017]
Judge's note: Checked on the page 8 image: the citation reads "[2017]" although no author is named in the running text, and the next citation repeats the authors ("Hedman et al. [Hedman et al. 2018]"). Pages 1 and 3 cite the same dataset as "Knapitsch et al. 2017", and the reference list has that entry. Citation formatting slip (year-only form used where the authors are not in the sentence); the reader can still find the reference.
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Typo Metric name written "L-PIPS" in the text ("using the standard PSNR, L-PIPS, and SSIM metrics") but "LPIPS" in Table 1, Tables 6 and 9 and Appendix D.
- p. 8 Sec. 7.2, Real-World Scenes
PSNR, L-PIPS, and SSIM
- p. 8 Table 1 header
𝐿𝑃𝐼𝑃𝑆↓
Judge's note: Page 8 image shows "L-PIPS" with a hyphen in Sec. 7.2 and "LPIPS" in the Table 1 header; page 14 uses "LPIPS" in table captions and text. Inconsistent spelling of one term, cosmetic.
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Typo "from our own runs of the author’s code for all previous methods" should read "authors’ code".
- p. 8 Sec. 7.2
from our own runs of the author’s code for all previous meth-
Judge's note: Page 8 image confirms the singular possessive "author’s" with the plural "all previous methods". Apostrophe placement error.
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Typo Row labels are "Ours-7K" / "Ours-30K" in Tables 1 and 2 but "Ours-7k" / "Ours-30k" in Tables 4-9.
- p. 8 Table 1
Ours-7K
- p. 14 Table 4
Ours-7k
Judge's note: Page 8 image shows capital K in Table 1 (and Table 2); page 14 image shows lower-case k in all six appendix tables. Cosmetic inconsistency in labels for the same configurations.
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Typo Footnote 2: "Note that A100’s are faster than A6000 GPUs." uses an apostrophe for a plural.
- p. 9 Footnote 2
Note that A100’s are faster than A6000 GPUs.
Judge's note: Page 9 image confirms "A100’s". Some style guides allow an apostrophe for plurals of alphanumeric designations, so this is a style point rather than a clear error; "A100s" would be the usual form.
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Typo Fig. 11 caption: "anisoptropic Gaussians" should read "anisotropic Gaussians".
- p. 11 Fig. 11 caption
anisoptropic Gaussians
Judge's note: Page 11 image shows "anisoptropic" in the Fig. 11 caption; the word is spelt "anisotropic" everywhere else (e.g. Fig. 10 caption on the same page). Not an extraction artefact.
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Typo "Compression techniques for point clouds is a well-studied field": plural subject with singular verb.
- p. 11 Sec. 7.4 Limitations
Compression techniques for point clouds is a well-
Judge's note: Page 11 image confirms the sentence as quoted. Subject-verb disagreement ("techniques ... is"); "Compression of point clouds is" or "techniques ... are" would be correct.
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Typo Acknowledgments: "P. Hedman and A. Tewari for proof-reading earlier drafts also T. Müller, A. Yu and S. Fridovich-Keil for helping with the comparisons" lacks a conjunction or punctuation before "also".
- p. 11 Acknowledgments
proof-reading earlier drafts also T. Müller
Judge's note: Page 11 image confirms the text as quoted: the list runs on without a comma or "and" between "earlier drafts" and "also T. Müller". Missing word or punctuation.
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Typo One author's surname is spelt three ways in the reference list: "Michael Zollhofer" (Lassner 2021 and Sitzmann 2019 entries), "Michael Zollhoefer" (Lombardi 2021 entry) and "Michael Zollhöfer" (Thies 2019 entry).
- p. 12 References, Lassner entry
Christoph Lassner and Michael Zollhofer. 2021.
- p. 12 References, Lombardi entry
Michael Zollhoefer
- p. 12 References, Thies entry
Michael Zollhöfer
Judge's note: Page 12 image shows all three spellings in the entries named; in-text citations use "Lassner and Zollhofer 2021". The inconsistency is internal to the paper and needs no outside fact; which form is right for each source is cosmetic (the umlaut form in the Thies entry is presumably the name).
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Typo Appendix C, Sorting: "We assign a key for each splats instance with up to 64 bits" — 'splats' should be singular ('each splat instance').
- p. 13 Appendix C, Sorting
We assign a key for each splats instance with up to 64 bits
Judge's note: Read on the page 13 image (right column, Appendix C): the sentence is printed as quoted. The plural after 'each' is a grammatical slip; the meaning is clear. Cosmetic.
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Typo Plenoxels garden and room cells in Tables 4–6 are printed to four decimals ("0.6063", "0.8417", "23.4947", "0.3864", "0.4186") while every other measured cell has three; in Table 5 only the garden cell is affected (room is 27.594).
- p. 14 Table 4, Plenoxels, garden and room
0.6063
- p. 14 Table 5, Plenoxels, garden
23.4947
- p. 14 Table 6, Plenoxels, garden and room
0.3864
Judge's note: Checked Tables 4–6 on the page 14 image and crops. Table 4 Plenoxels: garden 0.6063, room 0.8417; Table 5 Plenoxels: garden 23.4947 (room is 27.594, three decimals); Table 6 Plenoxels: garden 0.3864, room 0.4186. All other cells have three decimals, or two in the copied Mip-NeRF360† PSNR row. Formatting inconsistency only; no value is shown to be wrong.
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