Adaptive Embedding Pattern for Grayscale-Invariance Reversible Data Hiding

Erdun Gao; Xinyi Gao; Zhibin Pan

REVIEW 4 major objections 4 minor 28 references

Adaptive Embedding Pattern for Grayscale-Invariance Reversible Data Hiding

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that adaptive one- or two-bit embedding with a two-level predictor improves grayscale-invariant reversible data hiding, gaining about 1.17 dB over the prior method at 50,000 bits.

desk verdict Plausible incremental RDH method with a real ~1 dB gain, but garbled equations and a missing reversibility proof make this version unverifiable. read the letter →

arxiv 1908.05965 v1 pith:6SVKWGZF submitted 2019-08-16 cs.MM

Erdun Gao , Zhibin Pan , Xinyi Gao This is my paper · ORCID

classification cs.MM

keywords reversibledatahidingcolorimagegrayscaleinvarianceadaptiveembeddingpatterntwo-levelpredictorprediction-errorexpansionPSNRunitdistortion

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that reversible data hiding in color images can be made both higher-capacity and less distorting while preserving the image's grayscale exactly. The key idea is to treat each three-channel pixel as a unit and let the local smoothness decide whether to embed one or two secret bits in the red channel, with the blue channel carrying an error-correcting bit and the green channel recomputed to keep the rounded grayscale value unchanged. A two-level predictor re-estimates the pixel after the first embedding, which shrinks the error of the second embedded bit. On four standard test images, the paper reports average marked-image quality gains of 1.17 dB at 50,000 bits and 0.89 dB at 150,000 bits over the earlier grayscale-invariance scheme [1].

What carries the argument

The central mechanism is the adaptive embedding unit together with the two-level predictor. Each unit's region type is determined by the variance of the current grayscale pixel and its four neighbors; because the grayscale is invariant, the decoder can reproduce this classification. The red channel is modified by prediction-error expansion, the blue channel is used for the error-correcting bit, and the green channel is recomputed from the marked red and blue values by Eq. (22), $g = \mathrm{round}((gr - 0.299r - 0.114b)/0.587)$, to hold the rounded grayscale fixed. The two-level predictor averages the median-edge detector and accurate gradient selective prediction outputs for the first bit, then re-predicts the first marked value with the closer of the two predictors before embedding the second bit, which shrinks the second prediction error and thereby the overall distortion.

What would settle it

Run the described encoder on a natural image, then scan every marked unit and compare the grayscale computed by Eq. (5) with the original; any change outside the first auxiliary units would falsify the invariance claim. A simpler arithmetic check is to enumerate all red/blue modifications produced by the embedding rules and test whether a green value in $[0,255]$ satisfying Eq. (5) exists for every case; the first counterexample would refute the central claim.

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Extended reading notes

Core claim

The paper's central claim is that the previous one-bit-per-unit grayscale-invariance scheme can be improved without sacrificing invariance by making the embedding pattern adaptive. Units classified as smooth embed two secret bits into the red channel; normal units embed one bit; complex units embed none. The blue channel carries the preceding unit's error-correcting bit, and the green channel is set so that $\mathrm{round}(0.299r+0.587g+0.114b)$ stays identical to the original grayscale. The paper also introduces a two-level predictor: the first prediction is the average of two standard predictors (the median-edge detector and the accurate gradient selective prediction), and the second prediction re-predicts the already-marked red value using whichever of the two predictors is closer to it. The authors argue this reduces the unit embedding distortion and verify the improvement with PSNR comparisons at two payloads on four images.

Load-bearing premise

The load-bearing premise is that after the red and blue channels are modified, for every unit there is always an integer green value in $[0,255]$ that keeps the rounded grayscale exactly unchanged; the paper supplies Eq. (22) for that value but does not prove it always exists or that the error-correcting bit is enough to recover the original after two-bit embedding.

Editorial extensions

If this is right

If the claimed gains hold, the same grayscale-invariance guarantee as the baseline is obtained with higher marked-image quality at equal payload, which widens the usable capacity of feature-preserving reversible data hiding.
Because the decoder can reconstruct the region classification from the invariant grayscale, the adaptive pattern adds no side information beyond the two thresholds and the compressed location map.
The two-level re-prediction reduces the second embedding error, so the benefit should grow as more smooth-region units are available and shrink on highly textured images, matching the paper's small gain on Baboon.
The method still cannot match the raw PSNR of non-invariance color reversible data hiding schemes such as guided-filtering RDH, but it preserves the grayscale structure those schemes do not, so the comparison is a trade-off rather than an outright win.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct extension suggested by the pattern is to allow three or more bits in very flat regions, with a correspondingly deeper predictor chain; the paper does not explore this.
The invariance guarantee covers only the rounded integer grayscale, not the continuous $0.299R+0.587G+0.114B$ sum; applications needing exact linear grayscale would require stricter control of the green channel.
The first few units are excluded from invariance because they carry auxiliary bits; relocating the auxiliary data or embedding it inside the secret stream could make the invariance claim hold for the whole marked image.
The two-level predictor's gain depends on the two base predictors disagreeing enough that re-predicting helps; a testable prediction of this paper's mechanism is that the advantage will be largest on images where those two predictors diverge frequently.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the adaptive one/two-bit embedding plus two-level predictor is a plausible incremental improvement over Hou et al., and the reported ~1 dB gain at fixed capacity may be real. But as written the paper is not verifiable: the key equations are garbled, the reversibility argument is missing, and the experiments are too thin to take the numbers as established.

What's actually new: embedding one or two bits into R depending on local complexity, and re-predicting after the first embedding so the second embedding step uses a smaller prediction error. That combination is not in the cited papers, and the worked UED examples are arithmetically consistent. The idea of protecting the grayscale while carrying more payload in smooth regions is a legitimate contribution to this niche.

Soft spots, in order of severity:

1. Eqs. (15)-(16) are nearly unreadable and contain an undefined "NULL otherwise" branch. No one can check the two-level embedding/extraction without guessing what the authors intended.

2. There is no proof of reversibility. The G-recovery step is especially under-specified. The stress-test concern about Eq. (22) does not land as stated if R and B are recovered before G, as Fig. 13 suggests; the equation should then use restored R and B. But the paper never says this explicitly, and the variable names say "marked." The authors need to state the extraction order and prove that the two-level prediction loop is lossless.

3. Experiments: four images, no code, no threshold values, no error bars, only one baseline. That may be acceptable for a short paper in this subfield, but it does not support "significantly" beyond a small margin.

4. Minor: the first few units' grayscale is not invariant; the paper admits this, so it is not a hiding flaw.

Bottom line: the idea has merit and the central mechanism is probably sound, but the presentation is not referee-ready. It deserves review rather than desk rejection; a serious referee should ask for a clean algorithm statement, a reversibility proof, and a slightly broader evaluation. I would not cite it in this form.

Referee Report

4 major / 4 minor

Summary. The paper proposes an adaptive embedding pattern and a two-level predictor for color-image reversible data hiding (RDH) that aims to preserve the grayscale of the cover image. For pixels in smooth regions, two secret bits are embedded into the red channel, while the blue channel carries an error-correcting bit and the green channel is adjusted to keep the grayscale invariant. The method is compared experimentally with Hou et al.'s grayscale-invariance RDH scheme on four test images, with average PSNR improvements of 1.17 dB at 50,000 bits and 0.89 dB at 150,000 bits claimed. The central claims are that the scheme is reversible, that the grayscale is invariant except for a small number of auxiliary-information units, and that the adaptive pattern and two-level predictor improve embedding performance.

Significance. If the claims are correct, the work would be a useful extension of grayscale-invariant RDH, particularly the idea of embedding two bits in smooth regions and re-predicting between the two embedding steps. The unit-embedding-distortion rationale is clearly stated, and a direct comparison with the prior method of Hou et al. is appropriate. The paper also honestly notes the exception that the first few units carrying auxiliary information are not grayscale-invariant. However, the manuscript does not include machine-checked proofs or code, and as written it contains a potentially load-bearing error in the green-channel extraction formula, internally inconsistent worked examples, and an under-specified two-level predictor. These issues currently prevent the claimed contributions from being verified.

major comments (4)

[III.E, Eq. (22)] Equation (22) is the only stated rule for restoring the green channel, and it uses the marked red and blue values r_marked and b_marked. Because the embedding procedure first changes R and B and then adjusts G so that gr = round(0.299 r_marked + 0.587 g + 0.114 b_marked), the integer g returned by Eq. (22) is the adjusted value G' rather than the original cover value G. For example, from cover (100,100,100) with gr = 100, if embedding produced (r_marked, b_marked) = (104,100), the only g that preserves gr is 98; Eq. (22) returns 98, while the original G is 100, and 100 is not a feasible solution of the grayscale equation for the marked pair. The error-correcting bit cannot disambiguate this case because the original G is not among the candidate values for the marked R and B. No condition, location-map entry, or auxiliary bit is provided that excludes or encodes these cases, so the scheme is not shown to be reversible. If the intended extraction uses the recovered original R and B values, Eq. (22) must be corrected accordingly and a full reversibility proof must be supplied.
[III.D, Figs. 9-13] The worked examples intended to illustrate the method do not satisfy the central grayscale-invariance property. In the smooth-region example of Fig. 9 (repeated in Fig. 11), the original unit (103,86,96) has grayscale round(0.299*103 + 0.587*86 + 0.114*96) = 92, while the marked unit (104,93,86) has grayscale round(0.299*104 + 0.587*93 + 0.114*86) = 95. The normal-region example in Fig. 12 is similarly inconsistent with the stated grayscale preservation. Since grayscale invariance is the defining contribution of the paper, these examples must be recomputed and made consistent; as printed, they undermine confidence in the implementation and in the reported experimental results.
[III.B, Eqs. (15)-(16)] The two-level predictor is not specified precisely enough for a reader to implement or verify it. The equations are garbled: P1, P2, P_min, P_max, and "NULL" are not properly defined; the selection rule for P2 is incomplete; and the extraction equations for the two-bit case are not given. The paper also does not prove that the decoder can uniquely recover the first marked value and both embedded bits from the final marked red value, nor does it show that the prediction context (the neighboring pixels) is identical at the embedder and the extractor under the assumed embedding order. A complete algorithmic description and a formal reversibility argument for the two-level predictor are needed.
[IV, Tables I-II] The experimental support for the headline claim is thin. Results are reported for only four images with no standard deviations, no repeated trials, and no statistical test, so the word "significantly" in the abstract is not justified statistically. The paper also does not quantitatively report how many units actually change grayscale or measure the grayscale error, despite the exception admitted in Section III.E. The comparison should include error bars for the four images, a clear statement of whether the payload counts secret bits only or includes auxiliary information, and a quantitative report of grayscale preservation.

minor comments (4)

[Eqs. (5), (17), (18)] Several equations are corrupted by formatting: Eq. (17) is not a correct PSNR formula as printed (the standard form is 20 log10(255/sqrt(MSE))), and Eq. (18) is missing parts of the summation notation. These need to be typeset correctly.
[Eq. (22)] The coefficient 0.144 appears in the printed Eq. (22), whereas the grayscale formula in Eq. (5) uses 0.114 for the blue channel; this inconsistency must be fixed.
[Abstract and III.E] The abstract claims grayscale invariance without qualification, but Section III.E admits that the first (16 + 2*ceil(log2 N))/3 units change grayscale; this exception should be stated in the abstract and in the conclusions.
[Throughout] There are numerous typos and grammatical errors, such as "superoitiry", "prediciton", and "orginal", and the labels in Figures 2 and 13 are hard to read; a careful proofreading and figure revision are needed.

Circularity Check

1 steps flagged · score 6.0 of 10

Eq. (22) recovers the adjusted green G', not the cover G; the claimed reversibility step is circular by construction.

self definitional [Section III.D (Extraction example), Eq. (22)]
"From the ECB of last unit and the grayscale, the original value could be calculated as (( 0.299 0.144 ) / 0.587)original marked markedg round gr r b= − − (22)"

At embedding, the green channel is modified to a value G' satisfying round(0.299 R' + 0.587 G' + 0.114 B') = gr, the invariant grayscale. Eq. (22) is exactly this same equation solved for G using the marked R' and B' and the invariant gr. Its output is therefore G', the adjusted green, not the cover green. Labeling this output 'the original value' defines the cover value to be the adjusted value instead of recovering it. In any unit where G had to change, the cover G is not a solution of Eq. (22), and no location-map entry or ECB use excludes those units. The extraction claim is thus forced by the definition of the adjustment, not derived from cover data.

full rationale

The paper's main experimental comparison is not circular: PSNR gains are measured against the external method [1] on standard test images, and the thresholds T1/T2 are transmitted as auxiliary information rather than fitted to the reported output. No self-citation chain is load-bearing (references [1], [26], [27], [28] are external). The single circular step is localized to the extraction formula Eq. (22), which inverts the grayscale-preservation equation used to define G'. That makes the recovery of the 'original' green value self-definitional and invalidates the reversibility claim for any unit where G' differs from the cover G. Because this step is central to the reversible-data-hiding claim, the circularity score is elevated to 6; the distortion-capacity comparison itself remains an independent empirical result.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on two unstated assumptions: the always-possible green-channel adjustment and the unique decodability of the two-predictor selection. The only free parameters are the two complexity thresholds, whose values are not reported.

free parameters (2)

T1 = not reported
Threshold for classifying complex vs normal regions; transmitted as 8-bit auxiliary information; value chosen by authors but not disclosed.
T2 = not reported
Threshold for classifying normal vs smooth regions; transmitted as 8-bit auxiliary information; value chosen by authors but not disclosed.

assumptions (4)

domain assumption The grayscale conversion formula (Eq. 5) with rounding is fixed and shared by encoder and decoder.
Used in Eq. (22) to adjust green channel; if the grayscale metric differs, the invariance and reversibility fail.
domain assumption For every unit, an integer green value exists in [0,255] that restores the original grayscale after red and blue modifications.
Eq. (22) computes the green value with round(); the paper does not prove existence or uniqueness. This is load-bearing for grayscale invariance.
ad hoc to paper The two-level predictor selection (min/max of MED and AGSP) can be uniquely recovered at decoding.
Eq. (16) has a 'NULL otherwise' branch that is not defined; the decoder's ability to know which predictor was used is essential for reversibility.
domain assumption The complexity measure Delta computed on invariant grayscale is unchanged by embedding.
Encountered in Section III.C; if grayscale changes for the first units, those units are excluded, but the paper does not fully analyze boundary effects.

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Cite this review

Pith. "Pith review of Adaptive Embedding Pattern for Grayscale-Invariance Reversible Data Hiding." pith.science (2026). https://pith.science/paper/6SVKWGZF

@misc{pith2026190805965,
  author       = {Pith},
  title        = {Pith review of: Adaptive Embedding Pattern for Grayscale-Invariance Reversible Data Hiding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6SVKWGZF}},
  note         = {Machine review of arXiv:1908.05965}
}

read the original abstract

In traditional reversible data hiding (RDH) methods, researchers pay attention to enlarge the embedding capacity (EC) and to reduce the embedding distortion (ED). Recently, a completely novel RDH algorithm was developed to embed secret data into color image without changing the corresponding grayscale [1], which largely expands the applications of RDH. In [1], for color image, channel R and channel B are exploited to carry secret information, channel G is adjusted for balancing the modifications of channel R and channel B to keep the invariance of grayscale. However, we found that the embedding performance (EP) of that method is still unsatisfied and could be further enhanced. To improve the EP, an adaptive embedding pattern is introduced to enhance the competence of algorithm for selectively embedding different bits of secret data into pixels according to context information. Moreover, a novel two-level predictor is designed by uniting two normal predictors for reducing the ED for embedding more bits. Experimental results demonstrate that, compared to the previous method, our scheme could significantly enhance the image fidelity while keeping the grayscale invariant.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

D. Hou, W . Zhang, K. Chen, S.J. Lin, N. Y u, Reversible Data Hiding in Color Image with Grayscale Invariance, IEEE Transactions on Circuits & Systems for Video Technology. PP (2018) 1–1

work page 2018

[2] [2]

J. Li, X. Li, B. Yang, X. Sun, Segmentation -Based Image Copy -Move Forgery Detection Scheme, IEEE Transactions on Information Forensics and Security. 10 (2015) 507–518

work page 2015

[3] [3]

H. Kai, D. Li, Trusted Cloud Computing with Secure Resources and Data Coloring, IEEE Internet Computing. 14 (2010) 14–22

work page 2010

[4] [4]

Coatrieux, G.C

G. Coatrieux, G.C. Le, J.M. Cauvin, C. Roux, Reversible watermarking for knowledge digest embedding and reliability control in medical images, IEEE Transactions on Information Technology in Biomedici ne A Publication of the IEEE Engineering in Medicine & Biology Society. 13 (2009) 158

work page 2009

[5] [5]

Tian, Reversible data embedding using a difference expansion, Circuits & Systems for Video Technology IEEE Transactions On

J. Tian, Reversible data embedding using a difference expansion, Circuits & Systems for Video Technology IEEE Transactions On. 13 (2003) 890–896

work page 2003

[6] [6]

Ni, Y .-Q

Z. Ni, Y .-Q. Shi, N. Ansari, W. Su, Reversible data hiding, IEEE Transactions on Circuits and Systems for Video Technology. 16 (2006) 354–362. doi:10.1109/TCSVT.2006.869964

work page arXiv 2006

[7] [7]

Sachnev, H.J

V. Sachnev, H.J. Kim, J. Nam, S. Suresh, Y.Q. Shi, Reversible Watermarking Algorithm Using Sorting and Prediction, IEEE Transactions on Circuits & Systems for Video Technology. 19 (2009) 989–999

work page 2009

[8] [8]

S. Weng, Y . Shi, W . Hong, Y . Yao, Dynamic improved pixel value ordering reversible data hiding, Information Sciences. 489 (2019) 136–154

work page 2019