U-Net: Convolutional Networks for Biomedical Image Segmentation
2015 · paper · AI and machine learning
Presents U-Net, a neural network with a contracting and a symmetric expanding path, trained with heavy data augmentation on very few images. It reportedly beat the prior best method on an electron microscopy segmentation challenge and won two 2015 cell tracking categories.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
1 finding
Substance Eq. (1) prints "E = Σ_{x∈Ω} w(x) log(p_ℓ(x)(x))" with no leading minus sign, yet the text calls it the cross-entropy that "penalizes at each position the deviation of p_ℓ(x)(x) from 1".
- p. 4 Section 3, Eq. (1)
E = Σ w(x) log(pℓ(x)(x))
Judge's note: The page 4 image confirms there is no minus sign. Reworking it: p_ℓ(x)(x) is a softmax output in (0,1], so log p ≤ 0. With w(x) ≥ 0 (a weight map), E ≤ 0, and E reaches its maximum of 0 when every p = 1. Training is by SGD minimisation (Section 3), and minimising this E would drive p towards 0. So the formula as printed does not penalise deviation from 1. The weighted cross-entropy the text describes is E = -Σ w(x) log p_ℓ(x)(x).
Second check: another model agreed
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7 minor (typos and the like; most checked by the judge only)
Typo Abstract, first sentence: "There is large consent that successful training" uses 'consent' (permission) where 'consensus' (agreement) is meant.
- p. 1 Abstract, first sentence
There is large consent that successful training
Judge's note: The page 1 image shows "There is large consent that successful training of deep networks requires many thousand annotated training samples." 'Consensus' is the intended word. This is a cosmetic wording slip.
Second check: none (judge only)
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Typo Fig. 2 caption: "seamless segmentation of arbitrary large images" should read 'arbitrarily large', as the body text on the same page has it.
- p. 3 Fig. 2 caption
seamless segmentation of arbitrary large images
- p. 3 Introduction, paragraph on overlap-tile
seamless segmentation of arbitrarily large images
Judge's note: The page 3 image shows the caption reading 'arbitrary large images', while the body text reads 'arbitrarily large images'. This is a cosmetic grammar slip.
Second check: none (judge only)
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Typo Section 4 says "achieve an average IOU of 77.5%" for DIC-HeLa, but Table 2 gives u-net 0.7756, which rounds to 77.6%.
- p. 7 Section 4, text
achieve an average IOU of 77.5%
- p. 7 Table 2, u-net row, DIC-HeLa
0.7756
- p. 7 Table 2 vs Section 4 text
average IOU of 77.5%
Judge's note: On page 7, Table 2's u-net DIC-HeLa value is 0.7756 and the text says 77.5%. This is consistent with truncation rather than rounding, whereas the 0.9203 in the same paragraph is rounded to 92%. The discrepancy is trivial.
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Typo Misspelling: "This segmenation task is part of the ISBI cell tracking challenge" should read 'segmentation'.
- p. 7 Section 4, second paragraph
This segmenation task is part of the ISBI cell tracking challenge
Judge's note: The misspelling 'segmenation' is visible on the page 7 image.
Second check: none (judge only)
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Typo Misspelling: "U373 cells on a polyacrylimide substrate" should read 'polyacrylamide'.
- p. 7 Section 4, PhC-U373 description
U373 cells on a polyacrylimide substrate
- p. 7 Experiments, para 3
polyacrylimide substrate
Judge's note: The page 7 image shows 'polyacrylimide'. The standard name of the substrate material is polyacrylamide.
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Typo Section heading misspelled: "Acknowlegements" should read 'Acknowledgements'.
- p. 8 Section heading
Acknowlegements
Judge's note: The page 8 image shows the heading printed as 'Acknowlegements'.
Second check: none (judge only)
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Typo Reference 4 lists "Hariharan, B., Arbelez, P., Girshick, R., Malik, J."; the co-author's name appears to be Arbeláez.
- p. 8 Reference 4
Hariharan, B., Arbelez, P., Girshick, R., Malik, J.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the co-author of 'Hypercolumns for object segmentation and fine-grained localization' (arXiv:1411.5752) is Pablo Arbeláez. The page 8 image shows 'Arbelez', with both the accented 'á' and the letter it stands for missing. This is probably a BibTeX accent-encoding loss.
Second check: none (judge only)