NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis
Lecture Notes in Computer Science, 2020 · paper · Computer science
Represents a scene as a neural network mapping 3D position and viewing direction to density and color, optimized from images with known camera poses. Volume rendering produces novel views, which the authors report outperform prior view-synthesis work.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
4 findings
Substance Real-image resolution is given as "All images are 1008×756 pixels." in Section 6.1 but as "800 × 800 and 1008 × 752 respectively for the other methods" in Appendix B; Appendix A's "our real scenes require 762k rays per image" matches 1008×756.
- p. 10 Section 6.1, Real images of complex scenes
All images are 1008×756 pixels.
- p. 19 Appendix B, Quantitative Comparisons
800 × 800 and 1008 × 752 respectively
- p. 18 Appendix A, Rendering Details
our real scenes require 762k rays per image
- p. 19 Appendix B Quantitative Comparisons
1008 × 752 respectively
Only the authors can say what is right here.
Judge's note: Read page 10, 18 and 19 images. 1008×756 = 762,048, which matches the 762k rays; 1008×752 = 758,016. The SRN resolution of 504×376 in Appendix B is exactly half of 1008×752, so 752 may be a cropped evaluation height. I searched the text for "crop", "752" and "756" and found no statement of any cropping or of a second resolution. The two heights are therefore unexplained, and only the authors can say which applies where.
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Reference or label Section 6 cites "qualitatively (Figs. 8 and 6)" for the qualitative comparisons; Fig. 5, the main-body synthetic-scene comparison, is never cited in the running text, and Fig. 8 is the appendix DeepVoxels figure.
- p. 9 Section 6, first sentence
qualitatively (Figs. 8 and 6)
- p. 9 Section 6 Results, first sentence
qualitatively (Figs. 8 and 6) show that our
- p. 11 Fig. 5 caption
Fig. 5: Comparisons on test-set views for scenes from our new synthetic dataset
- p. 22 Fig. 8 caption
Comparisons on test-set views for scenes from the DeepVoxels [41] syn-
Only the authors can say what is right here.
Judge's note: Read page 9, 11 and 22 images. Fig. 5 (page 11) is the comparison on the new synthetic dataset and Fig. 6 the real scenes; Fig. 8 (page 22) is the DeepVoxels comparison in the appendix. A search of the text for "Fig. 5" finds only its own caption. Fig. 8 is a genuine qualitative comparison, so the pointer is not strictly false; the out-of-order "8 and 6" and the uncited Fig. 5 suggest "Figs. 5 and 6" (or 5, 6 and 8) was intended, which only the authors can settle.
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Reference or label Reference 5 lists the same author twice: "Cohen, M., Gortler, S.J., Szeliski, R., Grzeszczuk, R., Szeliski, R.: The lumigraph."
- p. 15 References, entry 5
Cohen, M., Gortler, S.J., Szeliski, R., Grzeszczuk, R., Szeliski, R.: The lumigraph.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the true author list and order of The Lumigraph (said by reviewers to be Gortler, Grzeszczuk, Szeliski, Cohen), which is needed to fix the entry. The duplication itself is visible on the page 15 image, where "Szeliski, R." appears twice in entry 5.
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Wording Eq. (8), third component of the product is printed as "−(f+n)/(f−n) z − (−2fn)/(f−n)", a double negative; multiplying row 3 of M by (x,y,z,1)ᵀ gives −(f+n)/(f−n)·z − 2fn/(f−n).
- p. 19 Appendix C, Eq. (8), right-hand side, third row
−(f+n)/(f−n) z − −2fn/(f−n)
- p. 19 Appendix C, Eq. (9), third row
(f+n)/(f−n) − 2fn/(f−n) · 1/(−z)
Only the authors can say what is right here.
Judge's note: Read Eq. 7-9 on the page 19 image. Row 3 of M is (0, 0, −(f+n)/(f−n), −2fn/(f−n)). Its product with (x,y,z,1)ᵀ is −(f+n)/(f−n)·z + (−2fn/(f−n)). The image shows a minus operator followed by a fraction whose numerator is −2fn, which equals +2fn/(f−n), so the step is false as printed. Dividing the correct product by −z gives (f+n)/(f−n) − 2fn/(f−n)·1/(−z), which is Eq. 9 as printed, and matches b_z = 2fn/(f−n) in Eq. 20. The error is confined to Eq. 8 and the stated results stand, hence S3.
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13 minor (typos and the like; most checked by the judge only)
Wording Section 3 says the "8 fully-connected layers ... outputs σ and a 256-dimensional feature vector" and that "one additional fully-connected layer (using a ReLU activation and 128 channels)" outputs RGB, whereas Fig. 7 and its caption show 8 ReLU layers, then "An additional layer outputs the volume density σ" and the feature vector, then the 128-channel ReLU layer, then "A final layer (with a sigmoid activation) outputs the emitted RGB radiance".
- p. 5 Section 3, second paragraph
with 8 fully-connected layers (using ReLU activations and 256 channels per layer), and outputs σ and a 256-dimensional feature vector
- p. 5 Section 3, second paragraph
passed to one additional fully-connected layer (using a ReLU activation and 128 channels) that output the view-dependent RGB color
- p. 18 Fig. 7 caption
An additional layer outputs the volume density σ
- p. 18 Fig. 7 caption
A final layer (with a sigmoid activation) outputs the emitted RGB radiance
Judge's note: Read page 5 and page 18 images. Fig. 7 shows eight 256 blocks joined by ReLU arrows, an orange (no activation) arrow to a ninth 256 block carrying σ, a 128 block, and a dashed sigmoid arrow to RGB. Section 3 describes 8 + 1 layers. The main text reads as a simplified summary of the appendix specification, so this is a minor consistency point, but the two descriptions do differ as printed.
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Wording Section 6.4 says "positional encoding (row 2) and view-dependence (row 3) provide the largest quantitative benefit followed by hierarchical sampling (row 4)", but on LPIPS in Table 2 row 4 (0.109) is marginally worse than row 2 (0.108), so the ordering holds only for PSNR and SSIM.
- p. 13 Section 6.4, discussion of rows 2–4
benefit followed by hierarchical sampling (row 4)
- p. 14 Table 2, rows 2 and 4, LPIPS column
0.109
Judge's note: Read page 13 and page 14 images. Table 2: row 2 is 28.77 / 0.924 / 0.108, row 3 is 27.66 / 0.925 / 0.117, row 4 is 30.06 / 0.938 / 0.109, complete model is 31.01 / 0.947 / 0.081. The stated ranking holds for PSNR and SSIM. On LPIPS, removing hierarchical sampling costs 0.028 against 0.027 for positional encoding, a 0.001 difference. This is a very minor overgeneralisation.
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Wording Appendix C uses t both for the top frustum bound ("r and t are the right and top bounds of the scene at the near clipping plane", Eqs. 7-9, 18 "a_y = −n/t") and for the ray parameter in o + td (Eqs. 10-16).
- p. 19 Appendix C, text after Eq. (7)
r and t are the right and top bounds of the scene at the near clipping plane
- p. 21 Appendix C, Eq. (18)
a_y = −n/t
- p. 21 Appendix C, last paragraph
for tn = −(n+oz)/dz
Judge's note: Checked pages 19-21 images. The symbol t is the top bound in Eqs. 7-9 and 18 and the ray parameter in Eqs. 10-16 and in the text after Eq. 16. The meaning is recoverable from context and the top-bound t is eliminated by Eq. 22, so this is a notational clash, not a mathematical error. The t_n on page 21 (parameter at which the ray meets the near plane) is close in meaning to the near bound used in the main text, so that part is weaker.
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Typo Subject-verb disagreement in Section 3: "one additional fully-connected layer (using a ReLU activation and 128 channels) that output the view-dependent RGB color" should read "outputs".
- p. 5 Section 3, second paragraph
channels) that output the view-dependent RGB color
Judge's note: Read page 5 image. The subject is the singular "one additional fully-connected layer" and the verb is printed as "output".
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Typo Unmatched closing parenthesis in Section 5: "as demonstrated in Section 6.4). We introduce".
- p. 7 Section 5, first paragraph
as demonstrated in Section 6.4).
- p. 7 Section 5, first paragraph
as demonstrated in Section 6.4). We introduce
- p. 7 Section 5 intro
as demonstrated in Section 6.4)
Judge's note: Read page 7 image. The sentence "However, we observe that these components are not sufficient for achieving state-of-the-art quality, as demonstrated in Section 6.4)." has no opening parenthesis.
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Typo Plural used for a single table in Section 6: "We quantitatively (Tables 1) and qualitatively" should read "Table 1".
- p. 9 Section 6, first sentence
We quantitatively (Tables 1)
- p. 9 Section 6 Results, first sentence
We quantitatively (Tables 1) and qualitatively
- p. 12 Fig. 6 caption
multiples renderings
- p. 9 Sec. 6 first paragraph
qualitatively (Figs. 8 and 6)
Judge's note: Read page 9 image; "(Tables 1)" is printed. The other points bundled into this cluster are judged elsewhere: "multiples renderings" under C010 and the "Figs. 8 and 6" pointer under C004.
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Typo Subject-verb disagreement in Section 5.3: "The optimization for a single scene typically take around 100–300k iterations" should read "takes".
- p. 9 Section 5.3, last sentence
The optimization for a single scene typically take around 100–
Judge's note: Read page 9 image; the text is printed as quoted.
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Typo Fig. 5 caption prints "Material’s non-Lambertian reflectance" and "stand and Material’s object edges", but the scene is labelled "Materials" in the figure and in Table 4; the possessive should be "Materials’".
- p. 11 Fig. 5 caption (two occurrences)
Material’s non-Lambertian reflectance
- p. 11 Fig. 5 caption
stand and Material’s object edges
Judge's note: Read page 11 image: the row label reads "Materials" and the caption twice reads "Material’s". The Table 4 column header on page 23 is also "Materials".
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Typo Fig. 6 caption: "Blending between multiples renderings" should read "multiple renderings".
- p. 12 Fig. 6 caption
Blending between multiples renderings
Judge's note: Read page 12 image; the caption is printed as quoted.
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Typo Reference 10 has an empty author slot: "Vlasic, D., , Freeman, W.T."
- p. 15 References, entry 10
Vlasic, D., , Freeman, W.T.
Judge's note: Read page 15 image; the doubled comma with nothing between is printed in entry 10 and is not an extraction artefact.
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Typo Missing preposition: "Substituting t = 0 and t′ = 0 Eqn. 10 directly gives our NDC space origin o′" should read "... t′ = 0 into Eqn. 10 ...".
- p. 20 Appendix C, text between Eq. (10) and Eq. (11)
Substituting t = 0 and t′ = 0 Eqn. 10 directly gives
Judge's note: Read on the page 20 image; the sentence is printed without "into".
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Typo Table 4 caption misspelling: "more complex gometry and non-Lambertian materials" should read "geometry".
- p. 23 Table 4 caption
more complex gometry
- p. 23 Table 4 caption
more complex gometry and non-
Judge's note: Seen in the Table 4 caption on the page 23 image; not an extraction artefact.
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Typo Table 6 bolds only one of two tied best values: Mic SSIM "0.980" (rows 8 and 9, only row 8 bold); Chair SSIM "0.967", Lego SSIM "0.961" and Lego LPIPS "0.050" (rows 8 and 9, only row 9 bold).
- p. 25 Table 6, SSIM, Mic column, rows 8 and 9
0.980
- p. 25 Table 6, SSIM, Chair column, rows 8 and 9
0.967
Judge's note: Checked Table 6 on the page 25 image. The printed values tie at three decimals in those four cells and only one of each pair is bold, with the bolded row differing between columns. Bolding was probably applied to unrounded values, which would be legitimate; the paper does not say. Cosmetic consistency point.
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