{"id":"ced05bbf-c842-47e9-95c3-46857b408a7a","arxiv_id":"1908.05965","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"An adaptive embedding pattern plus a two-level predictor improves the PSNR of grayscale-invariant reversible data hiding by about 1 dB over Hou et al.'s method.","lead":"This paper reports an improved reversible data hiding scheme for color images that preserves the grayscale version of the image while embedding secret data. The improvement comes from adaptively embedding one or two bits per pixel group and re-predicting after the first embedding to reduce distortion.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (22) computes G from marked R,B, so it returns the adjusted G', not the cover G; in any unit where G had to change, the original G is not a candidate and reversibility fails.","rationale":"The reader identified the existence of a valid green value and ECB sufficiency as the weakest assumption. My concern is sharper: even when a valid adjusted G' exists, Eq. (22) uses the marked R and B values, so it recovers the adjusted G' rather than the cover G. The synthetic counterexample shows a concrete, plausible embedding case where the original G is not among the candidates for the marked R,B, so no ECB can resolve the ambiguity. This is internally inconsistent with the reversibility requirement, not merely an unproven edge case. Because the central claim is that the proposed scheme is reversible and grayscale-invariant with improved fidelity, a broken extraction chain invalidates the headline comparison. I would reject the paper as written unless the check shows that the implementation actually uses the recovered original R,B in Eq. (22) and the authors correct the text and provide the missing proof of G recoverability.","tokens_in":10389,"tokens_out":20932,"duration_ms":199882,"concrete_test":"Run the paper's embedding and extraction on a single synthetic unit with cover (R=100,G=100,B=100), grayscale Y=100, smooth-region classification, and two-bit embedding that produces R'=104, B'=100 (e.g., first PE=+1 with sd1=1, second PE=+1 with sd2=1, and B PE=0 with ECB=0). Set G' by the grayscale-preservation condition (G'=98). Then apply the extraction exactly as specified, including Eq. (22) with r_marked=104, b_marked=100, gr=100, and check whether the recovered G is 100 or 98. If it is 98, the paper's stated extraction formula is demonstrably wrong. As a second check, run a full-image simulation on Lena, Airplane, Lake, and Baboon and count embedded units in which the original G is not among the integer candidates satisfying round(0.299 R'_marked + 0.587 g + 0.114 B'_marked)=gr; a nonzero count falsifies the reversibility claim.","verdict_should_be":"REJECT","load_bearing_attack":"The load-bearing flaw is in the extraction of the original green value. Eq. (22) computes g_original from the marked R and B values: g = round((gr - 0.299 r_marked - 0.114 b_marked)/0.587). But the marked R and B already contain the embedded modifications; the value that satisfies the grayscale equation for those marked values is the adjusted G' chosen at embedding, not the original G. In any unit where G had to be changed at all, the original G is generically not a solution of round(0.299 r_marked + 0.587 g + 0.114 b_marked)=gr. Example: cover (100,100,100) has gr=100. After two-bit embedding suppose r_marked=104, b_marked=100. The unique G' preserving gr is 98 (0.299*104+0.587*98+0.114*100=100.022 -> round 100; g=99 gives 100.609 -> 101). Eq. (22) returns 98, not 100. The ECB cannot help because 100 is not one of the candidate G values for the marked R,B (only 98 is). Hence the extracted image is not the cover, and the method is not reversible. Because two-bit embedding can shift R by +4 even with prediction errors of 1, this occurs in exactly the smooth regions the method targets. The paper gives no condition, location-map entry, or proof excluding these cases, so the reported PSNR advantages do not establish a valid reversible, grayscale-invariant RDH scheme.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":10720,"tokens_out":13508,"duration_ms":124829,"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":[{"comment":"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.","section":"III.E, Eq. (22)"},{"comment":"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.","section":"III.D, Figs. 9-13"},{"comment":"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.","section":"III.B, Eqs. (15)-(16)"},{"comment":"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.","section":"IV, Tables I-II"}],"minor_comments":[{"comment":"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.","section":"Eqs. (5), (17), (18)"},{"comment":"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.","section":"Eq. (22)"},{"comment":"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.","section":"Abstract and III.E"},{"comment":"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.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper currently contains a potentially fatal extraction error in Eq. (22) and internally inconsistent worked examples. I recommend major revision rather than outright rejection because the core idea may be salvageable: if Eq. (22) is corrected to use the recovered original R and B values, and if the two-level predictor is fully specified with a rigorous reversibility proof, the method could become valid. However, the authors must also recompute their examples and provide substantially stronger experimental evidence. If a correct reversibility argument cannot be supplied, the manuscript should not be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nWhat'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.\n\nSoft spots, in order of severity:\n\n1. 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.\n\n2. 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.\n\n3. 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.\n\n4. Minor: the first few units' grayscale is not invariant; the paper admits this, so it is not a hiding flaw.\n\nBottom 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.","headline":"Plausible incremental RDH method with a real ~1 dB gain, but garbled equations and a missing reversibility proof make this version unverifiable.","tokens_in":11225,"tokens_out":5896,"would_cite":false,"duration_ms":61973,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["reversible data hiding","color image","grayscale invariance","adaptive embedding pattern","two-level predictor","prediction-error expansion","PSNR","unit embedding distortion"],"falsifier":"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.","tokens_in":10183,"feed_emoji":"🖼️","tokens_out":6443,"duration_ms":55284,"temperature":0.7,"pith_summary":"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].","feed_headline":"Adaptive hiding keeps grayscale intact, gains 1.17 dB","feed_subtitle":"A two-level predictor and one- or two-bit-per-pixel embedding sharpen reversible data hiding on color images.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"The baseline grayscale-invariance method whose one-bit-per-unit embedding and grayscale-balancing framework this paper extends and compares against.","marker":"[1]"},{"why":"Supplies the adaptive prediction-error expansion and pixel-selection idea behind the two-bit embedding and the alternative comparison used in the unit example.","marker":"[26]"},{"why":"Defines the median-edge detector (MED) used as one of the two predictors averaged in the first level.","marker":"[27]"},{"why":"Defines the accurate gradient selective prediction (AGSP) used as the other predictor in the two-level predictor.","marker":"[28]"},{"why":"Provides the difference-expansion mechanism on which prediction-error expansion for embedding secret bits is based.","marker":"[5]"},{"why":"Used in the comparison to show that conventional high-PSNR color RDH methods do not preserve grayscale features, motivating the invariance constraint.","marker":"[22]"}],"fun_headline_variants":["Adaptive pattern boosts reversible hiding, keeps grayscale","Selective embedding improves reversible hiding, preserves grayscale","Two-level predictor sharpens grayscale-invariant RDH","Context-aware embedding keeps grayscale, cuts distortion","Grayscale-invariant hiding gains 1.17 dB with adaptive pattern"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive pattern boosts reversible hiding, keeps grayscale","Selective embedding improves reversible hiding, preserves grayscale","Two-level predictor sharpens grayscale-invariant RDH","Context-aware embedding keeps grayscale, cuts distortion","Grayscale-invariant hiding gains 1.17 dB with adaptive pattern"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000638,"raw_usage":{"total_tokens":2925,"prompt_tokens":918,"completion_tokens":2007,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":534,"completion_tokens_details":{"reasoning_tokens":1926}},"tokens_in":534,"tokens_out":2007,"duration_ms":14817,"temperature":1.0,"reasoning_tokens":1926,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:59:34.523820+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The baseline grayscale-invariance method whose one-bit-per-unit embedding and grayscale-balancing framework this paper extends and compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the adaptive prediction-error expansion and pixel-selection idea behind the two-bit embedding and the alternative comparison used in the unit example."},{"cited_title":"Seroussi G.,","cited_arxiv_id":null,"evidence_quote":"Defines the median-edge detector (MED) used as one of the two predictors averaged in the first level."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the accurate gradient selective prediction (AGSP) used as the other predictor in the two-level predictor."},{"cited_title":"Tian, Reversible data embedding using a difference expansion, Circuits & Systems for Video Technology IEEE Transactions On","cited_arxiv_id":null,"evidence_quote":"Provides the difference-expansion mechanism on which prediction-error expansion for embedding secret bits is based."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Used in the comparison to show that conventional high-PSNR color RDH methods do not preserve grayscale features, motivating the invariance constraint."}],"review_version":1}