Geng Report: Welding Defect Detection Algorithm Based on Feature Extraction and Extreme Value Search — Suspected Severe Mathematical and Methodological Flaws

Academic fraud report · Geng Detector

Summary

This report evaluates the paper 'Welding Defect Detection Algorithm Based on Feature Extraction and Extreme Value Search' by Liang Wei, Tao Liang, Zhang Guangxian, and Li Zhenhua, published in the Journal of Shandong University (Engineering Science), DOI 10.6040/j.issn.1672-3961.0.2014.013. The overall verdict is 'highly suspicious' (orange). Although the paper shows no typical biomedical image-manipulation markers, the core algorithmic derivations contain serious low-level mathematical contradictions. Specifically, Equation (2) purports to be median filtering but the textual description defines mean filtering, and the formula itself erroneously combines a summation with a 'med' operator. Equation (1), intended as temporal frame averaging, illegally sums over the spatial indices i and j, leaving the left-hand side coordinate undefined. In addition, the experimental section lacks any quantitative metrics such as detection rate, false-positive rate, or localization error, relying instead on qualitative visual inspection of curves. Equipment dates (Varian Paxscan 2520, GE CC0 2505) are consistent with the 2014 publication date. Confidence in the reported flaws is high, as they are explicit textual and symbolic contradictions; however, image-based and statistical analyses were not possible due to input limitations.

Verdict

Highly suspicious (🟠). The paper contains severe, easily verifiable mathematical and logical errors in its core algorithmic formulas, combined with a near-total absence of quantitative experimental evidence. While no image-based fraud or timeline anomalies were detected, the methodological foundations are deeply flawed.

Key findings

Equation (2) logical contradiction: The text states that the template uses the *mean* of gray values ('使用模板内各像素点的灰度平均值'), which is the definition of mean filtering, yet the equation is labeled and framed as median filtering with an erroneous med ∑ operator — an undefined hybrid operation.
Equation (1) mathematical error: The temporal averaging formula is written as D(i,j) = (1/m) Σ_{i=1}^{h} Σ_{j=1}^{w} Σ_{t=1}^{m} F_t(i,j), which sums over the spatial coordinates that appear on the left-hand side, leaving the expression mathematically ill-defined for any pixel location.
No quantitative evaluation: The conclusion claims 'high detection accuracy' and other advantages, but the experimental section (Sections 3–4) provides no numerical table of detection rate, false-positive rate, mean squared localization error, or comparison with baseline algorithms.
Plausible timeline: Submission 2014-01-08, online publication 2014-05-30 (~5 months), consistent with normal peer-review cycles for Chinese engineering journals. Varian Paxscan 2520 and GE CC0 2505 X-ray equipment were commercially available before 2014.
Image / data forensic limitation: Provided text-only material did not include raw high-resolution figures or numeric data tables, so pixel-level image reuse, image splicing, and statistical-distribution tests could not be performed.

Evidence highlights

DOI: 10.6040/j.issn.1672-3961.0.2014.013
Equation (2) as written: G(i,j) = med Σ [A(i+s, j+t)] — the med (median) operator applied after a summation is not a standard image-processing operation and contradicts the paper's stated use of median filtering for salt-and-pepper noise.
Equation (1) as written: D(i,j) = (1/m) Σ_{i=1}^{h} Σ_{j=1}^{w} Σ_{t=1}^{m} F_t(i,j) — incorrect double spatial summation; the correct form should average over time only, e.g. D(i,j) = (1/m) Σ_{t=1}^{m} F_t(i,j).
Conclusion claims '较高的检测精度' and '检测精度高' with no supporting numeric metrics.
Figures 2, 3, and 5 are used as the sole experimental evidence, with narrative descriptions such as '趋于平缓' and '明显极大值点'.
Equipment: Varian Paxscan 2520 (commercially available since early 2000s), GE CC0 2505 portable X-ray unit (available before 2014).

Notes

The combined textual/equation contradiction in Section 2.1 strongly suggests either careless copy-paste from heterogeneous sources or insufficient understanding of the underlying image-processing operations, raising concerns about whether the algorithm was actually implemented and tested.
The reviewer recommends requesting the original source code and complete experimental datasets from the authors, and posting these concerns on PubPeer targeting Equations (1) and (2).
The journal's editorial office is advised to review the peer-review records of this paper, given that the mathematical derivations failed basic consistency checks.
Related publications by the same author group should be cross-checked for analogous formula mis-attribution.
All findings are derived solely from the provided text and the publicly available DOI metadata; image- and data-level forensic analyses were not feasible under the current input modality.