{"id":"5ef578f5-5fef-420c-a62b-68c15ad24d5e","arxiv_id":"2501.18929","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A training-free edge detector combining Sobel, heat-equation diffusion, and Canny/Laplacian fusion claims SOTA scores, but lacks reproducible evaluation and mislabels the diffusion equation as Schrödinger's.","lead":"A classical edge-detection pipeline labeled quantum-inspired, combining Sobel gradients, an iterative Laplacian diffusion step, and a max of Canny and Laplacian outputs, claims to beat deep learning methods on four standard edge benchmarks. The reported results are not reproducible from the paper, and the diffusion equation is not the Schrödinger equation.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The state-of-the-art claim rests on an edge map that cannot be thresholded as a soft confidence map: Eq. (22) takes the max of binary Canny with a raw Laplacian response, so the reported ODS/OIS/AP scores are not well-defined under the standard evaluation protocol.","rationale":"Read in good faith, the proposed method is a simple composition of classical operations: image diffusion (Eq. 6 is the heat equation despite the Schrodinger label), Gaussian blur, Canny detection, a Laplacian response, and a max fusion. The physics naming is inaccurate, but the empirical claim is the load-bearing part of the paper. That claim requires E_hybrid to be a soft edge-confidence map suitable for threshold-based evaluation. Eq. (22) fails this requirement because one operand is binary and the other is an unnormalized signed second-derivative response; thresholding such a map does not produce a meaningful precision-recall curve or standard ODS/OIS/AP scores. This is exactly the reader's weakest assumption. A full re-evaluation of Table II would settle the issue: an exact implementation with the standard benchmark code either reproduces the numbers or reveals that the tables are unvalidated. Since no code is provided, key parameters are unspecified, and ablations are run on single images, there is no evidence that changes the reader's REJECT verdict. No adjustment is needed.","tokens_in":17574,"tokens_out":4883,"duration_ms":48792,"concrete_test":"Implement Algorithm 1 exactly on the BSD500 test set, using the stated Canny thresholds t_low=50 and t_high=150, and feed E_hybrid from Eq. (22) into the standard BSDS evaluation code. First inspect the precision-recall curve: if it shows a flat segment for thresholds below 1, then E_hybrid is not a valid soft edge map. Then compare the resulting ODS/OIS/AP values to Table II. If the implementation reproduces 0.856/0.879/0.899 with the standard protocol, the empirical claim survives; if the numbers differ, or if matching them requires an unstated normalization or alternative fusion rule, the state-of-the-art claim across all tables is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the training-free method reaches state-of-the-art ODS/OIS/AP on four benchmarks. This requires the output of Eq. (22), E_hybrid = max(E_canny, E_lap), to be a soft edge-confidence map whose thresholds yield the precision-recall curves used by standard benchmarks. It is not. E_canny is binary {0,1} by Eq. (19); E_lap is the raw discrete Laplacian of the blurred image (Eqs. 20-21), unnormalized and signed. For any threshold tau < 1, all binary Canny edges are classified as positive along with positive Laplacian pixels; for tau > 1, no Canny edge survives unless E_lap exceeds tau. The resulting precision-recall curve has flat and degenerate segments, so it is not a monotone ranking by edge strength. Consequently the ODS, OIS and AP values in Tables I-IV are not computable from the published method without an undocumented post-processing step such as clipping, normalization, or using E_lap alone. No code or parameter values for delta, T, and sigma are supplied, and the ablations use single images, so the reported margins over trained deep networks cannot be independently checked.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a training-free edge detection pipeline composed of (i) Sobel gradient computation, (ii) iterative refinement by a Laplacian-based update starting from the grayscale image, and (iii) a hybrid edge map formed by taking the maximum of a Canny binary edge map and a Laplacian response. It reports state-of-the-art ODS/OIS/AP/F-measure numbers on NYUD, BSD500, Multicue, and PASCAL, and it includes ablations on BIPED images, noise robustness experiments, and runtime measurements. The central claim is that this classical, non-learned pipeline outperforms trained deep networks without any training.","tokens_in":17933,"tokens_out":4378,"duration_ms":37909,"significance":"If the reported results were valid, the paper would make a striking claim: a simple parameter-controlled classical pipeline surpassing deep edge detectors on standard benchmarks, with implications for low-resource edge detection. The claimed significance, however, depends entirely on (a) the iterative equation being correctly identified and analyzed, (b) the final edge map being a valid soft edge-confidence map for the standard threshold-sweep evaluation, and (c) the reported numbers being reproducible from specified parameters. As detailed below, none of these conditions is met in the manuscript. The paper is also notable for what it does not ship: no code, no parameter values for delta, T, or sigma, and no evaluation-protocol details.","major_comments":[{"comment":"Equation (6), ∂ψ/∂t = δ∇²ψ, is the linear heat (isotropic diffusion) equation, not the Schrödinger equation. The time-dependent Schrödinger equation is first-order in time and contains an imaginary unit, e.g., iħ∂ψ/∂t = -(ħ²/2m)∇²ψ + Vψ. The paper never introduces a potential term or complex phase, so the 'quantum-inspired' label is not supported by the mathematics. This is load-bearing because the claimed novelty of the refinement stage rests on the Schrödinger analogy.","section":"§III-B, Eq. (6)"},{"comment":"The discrete implementation is not the PDE in Eq. (6). Eq. (7) computes ψ(t+Δt) = ψ(t) + δ∇²ψ(t), but Δt is never defined; the text simply uses δ as both diffusion coefficient and effective step size. Eq. (9) clips the result to [0,255] after every iteration, which makes the iterates a projected diffusion process rather than a solution of Eq. (6). No convergence, stability, or qualitative invariance under clipping is shown. Since this iteration is the entire preprocessing module, the manuscript must specify δ and T; it does not. Without these values the reported benchmark numbers cannot be reproduced.","section":"§III-B, Eqs. (7)–(9)"},{"comment":"The final edge map defined by Eq. (22), E_hybrid = max(E_canny, E_lap), is not a soft edge-strength map. By Eq. (19), E_canny is binary {0,1}, while E_lap from Eqs. (20)–(21) is an unnormalized, signed second-derivative response. For any threshold τ < 1, every Canny edge pixel is classified as a positive detection regardless of E_lap; for τ > 1, only pixels with E_lap > τ are kept and all Canny edges are discarded. The precision-recall curve is therefore not a monotone ranking of boundary confidence, and the ODS/OIS/AP values in Tables I–IV are not well-defined from the published method. Algorithm 1's 'clip(∇²I_blurred,0,255)' does not fix this, because clipping does not make the binary component a graded response. An undocumented normalization or post-processing step would be needed to compute the reported scores.","section":"§III-C, Eq. (22)"},{"comment":"The quantitative claims are not reproducible from the manuscript. No evaluation details are reported: the paper does not state which test split is used for BSD500 or PASCAL, how boundaries are matched to ground truth (e.g., the standard BSDS tolerance protocol), or how ODS/OIS/AP are computed. The free parameters of the pipeline—δ, T, σ, and the Canny thresholds—are not specified except for two threshold values in the text; the ablations in Section V are computed on single images (RGB_025.png and butterfly.png), so dataset-level metrics such as ODS cannot be meaningfully reported for those tables. The reported state-of-the-art margins therefore cannot be verified independently.","section":"§IV-B, Tables I–IV; §V"}],"minor_comments":[{"comment":"Reference numbering is inconsistent: in the text, 'EDTER [67]' should be [55], 'BDCN [64]' should be [52], and several other in-text citations do not match the reference list.","section":"§IV-B"},{"comment":"The paper contains an unfinished template header, '> REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) <', indicating a missing editorial step.","section":"Header"},{"comment":"Figure 3 is described in the text as comparing Roberts, Sobel, Prewitt, Canny, Edge-Net, and the proposed model, but the caption and surrounding discussion do not connect these to the quantitative noise tables; the qualitative results could be clearer.","section":"Fig. 3"},{"comment":"The abstract claims evaluation on BIPED, but BIPED is not included in the quantitative benchmark tables (Tables I–IV); it appears only in the single-image ablation.","section":"Abstract and §IV"},{"comment":"Section II's enumerated items are numbered as top-level list items (1–6), which produces confusing cross-references and is inconsistent with the rest of the paper's section numbering.","section":"§II"}],"recommendation":"reject","confidential_remarks":"The manuscript is not ready for review in its current form: the central mathematical identification is incorrect, the edge map used for evaluation is not a soft confidence map, and the benchmark scores are not reproducible from the described procedure. I recommend reject rather than major revision because the reported state-of-the-art scores cannot be derived from the published method; any corrected version would need a different edge-combination rule, a full re-evaluation, and complete parameter specifications. There is also a fit concern: the paper claims quantum inspiration but uses classical diffusion, and the citation list contains many mismatches."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This one you can skip unless you want a case study in evaluation failures. The paper claims a training-free, \"quantum-inspired\" edge detector beats EDTER and other deep models on NYUD, BSD500, Multicue, and PASCAL by large margins. The claim is not credible. The method is a composition of Sobel, a heat-equation diffusion step mislabeled as the Schrödinger wave equation, and a max fusion of Canny and Laplacian responses. Nothing here is new except the benchmark numbers, and those numbers are not well-defined.\n\nThe one thing the paper does well is breadth: it evaluates on multiple datasets and compares against a long list of methods. That is why the arithmetic deserves a careful look. It does not survive. Equation (6) is the heat equation, not Schrödinger's; there is no imaginary unit or potential. Equation (9) clips the diffused intensity, so the discrete update no longer matches the stated PDE. But the load-bearing flaw is Equation (22): E_hybrid = max(E_canny, E_lap). E_canny is binary {0,1}, E_lap is a signed, unnormalized Laplacian response. No threshold sweep over this max produces a meaningful precision-recall curve. For thresholds below 1, every Canny edge is positive regardless of strength; above 1, only Laplacian pixels survive. The ODS/OIS/AP values in Tables I–IV are therefore not computable from the published method unless an undocumented post-processing step exists. The algorithm box hints at clipping the Laplacian to [0,255], but that still does not make the max a monotone confidence map.\n\nThe free parameters—diffusion coefficient, iteration count, Gaussian sigma, Canny thresholds—are never specified. There is no code, no error bars, and the ablations are on single images. The reported margins over trained deep networks are implausibly large, and without the missing details there is no way to reproduce them.\n\nWho is this paper for? Not for anyone building or benchmarking edge detectors. It could be a cautionary example in a methods course. It does not deserve a full peer review in its current form. If the authors supplied code, fixed the fusion to produce a genuine soft edge map, and tested on a proper validation split, there might be a modest conference paper about parameter-free classical edge detection—but that is speculative. My recommendation: desk reject.","headline":"A training-free edge detector made of Sobel, heat-equation diffusion, and a Canny/Laplacian max-fusion whose benchmark scores are invalid because the final map is not thresholdable.","tokens_in":18396,"tokens_out":2765,"would_cite":false,"duration_ms":25599,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68U10","68T45"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that a training-free pipeline of Sobel gradients, Schrödinger-inspired diffusion, and Canny-Laplacian fusion beats trained edge detectors on NYUD, BSD500, Multicue, and PASCAL.","keywords":["edge detection","training-free","quantum-inspired","Schrödinger wave equation","Canny edge detector","Laplacian operator","hybrid edge detection","edge benchmarks"],"falsifier":"Re-implement the pipeline exactly as Eqs. (3)–(22) specify, run it on a sample of NYUD, BSD500, Multicue, and PASCAL images, and evaluate the raw $E_{\\mathrm{hybrid}}$ map with the standard BSDS benchmark code; if the computed ODS/OIS/AP scores fall materially below the tables, or if the evaluation cannot handle the many tied values introduced by the binary Canny component, the central claim is refuted.","tokens_in":17367,"feed_emoji":"🖼️","tokens_out":10407,"duration_ms":86165,"temperature":0.7,"pith_summary":"The paper sets out to show that a fully classical, training-free pipeline can beat deep neural edge detectors on standard benchmarks. The method combines a Sobel gradient map, an iterative diffusion step inspired by the Schrödinger wave equation, and a hybrid fusion of Canny and Laplacian edges. If the reported numbers hold, high-accuracy edge detection would no longer require large labeled datasets or GPU training, which matters for medical imaging, autonomous systems, and remote sensing. The paper further claims the full model runs in about 0.22 seconds per image on modest memory, making it deployable on constrained devices.","feed_headline":"A training-free edge detector tops deep rivals on four benchmarks","feed_subtitle":"Quantum-inspired diffusion plus Canny-Laplacian fusion reports top ODS scores on four standard datasets.","key_machinery":"The load-bearing mechanism is the Schrödinger-inspired evolution step, implemented as the discrete diffusion update $\\psi(x,y,t+\\Delta t)=\\psi(x,y,t)+\\delta\\,\\nabla^2\\psi(x,y,t)$ with clipping to $[0,255]$, which smooths uniform regions while preserving and sharpening high-gradient edges. This refined image is then blurred with a Gaussian kernel and fed to two detectors: a Canny edge detector with thresholds $t_{\\mathrm{low}}=50$ and $t_{\\mathrm{high}}=150$, and a discrete Laplacian second-derivative response. The two edge maps are fused by the pointwise maximum $E_{\\mathrm{hybrid}}(x,y)=\\max(E_{\\mathrm{canny}}(x,y), E_{\\mathrm{lap}}(x,y))$, which is the step the paper credits for combining local and global edge evidence.","core_discovery":"The central claim is that a hand-crafted edge detector, computed by refining Sobel gradients with an iterative Laplacian diffusion step modeled on the Schrödinger wave equation and then taking the pixel-wise maximum of a Canny binary map and a raw Laplacian response, outperforms state-of-the-art trained edge detectors. On NYUD the paper reports ODS 0.823, OIS 0.856, AP 0.889, and F-measure 0.896, against 0.774 ODS for the transformer-based EDTER baseline. On BSD500 the reported ODS is 0.856 versus 0.824 for EDTER; on Multicue the reported ODS is 0.921 versus 0.894; on PASCAL the reported ODS is 0.801 versus 0.752 for the next-best RCN. The authors present these results as evidence that training-free, quantum-inspired classical processing can reach state-of-the-art edge extraction while offering noise robustness and computational efficiency.","pith_inferences":["A fair stress test of the claimed advantage would recalibrate the Canny and Laplacian outputs into a common confidence scale before fusion; if the margin over EDTER shrinks under calibration, the reported gains may be an artifact of the raw maximum rule rather than of the diffusion preprocessing.","The update in Eq. (7) is mathematically the classical heat equation, not the time-dependent Schrödinger equation, so the 'quantum-inspired' framing is an analogy; the paper's practical claims would still stand, but the method is better characterized as a classical PDE-based detector.","The refined image $\\psi(x,y,T)$ could be tested as a preprocessing front end for existing trained detectors; the ablation suggests the diffusion step may benefit downstream models without retraining."],"forward_implications":["If the reported scores hold, non-learned edge detection can surpass deep networks on four standard benchmarks, removing the need for labeled training data in edge-extraction applications.","The stated runtime and memory of 0.22 seconds and 65 MB on a single test image imply the method can run on embedded or low-power devices without specialized hardware.","The ablation tables imply the Schrödinger-inspired diffusion step is the main accuracy driver, adding about 0.085 ODS on the tested image compared with the same pipeline without it.","The noise-robustness experiments imply the method remains usable under Gaussian noise up to $\\sigma=40$, which would be valuable wherever clean images are not guaranteed."],"supporting_citations":[{"why":"Provides the HED deep-learning baseline and the evaluation convention the paper uses for ODS/OIS/AP/F-measure comparisons.","marker":"[2]"},{"why":"Supplies the BSD500 dataset and the gPb-ucm contour-detection baseline used in Tables I and II.","marker":"[7]"},{"why":"Supplies the NYUD dataset used in Table I.","marker":"[14]"},{"why":"Supplies the Multicue dataset used in Table III.","marker":"[13]"},{"why":"Supplies the PASCAL dataset used in Table IV.","marker":"[8]"},{"why":"The transformer-based EDTER detector is the strongest baseline the paper claims to surpass on NYUD, BSD500, and Multicue.","marker":"[55]"},{"why":"The RCF detector appears in all four comparison tables and anchors the claimed improvements over deep edge detectors.","marker":"[50]"},{"why":"Defines the Canny edge-detection algorithm and its thresholding protocol used in the hybrid fusion stage.","marker":"[15]"},{"why":"Supplies the BIPED dataset used for the ablation studies and qualitative comparison.","marker":"[12]"}],"fun_headline_variants":["Quantum-inspired edge detection beats deep nets with no training","Training-free detector outshines deep models on edge benchmarks","Schrödinger-powered edge detector surpasses trained rivals","No training: quantum-inspired method claims edge-detection crown","Lightweight edge detector bests deep learners on four datasets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported benchmark scores presuppose that the pointwise maximum of a binary Canny map and a raw Laplacian response is a valid, thresholdable edge-confidence map under the standard ODS/OIS/AP protocol; if that fusion is not such a map, the headline numbers would not be computable as published.","fun_headline_variants_meta":{"raw":{"variants":["Quantum-inspired edge detection beats deep nets with no training","Training-free detector outshines deep models on edge benchmarks","Schrödinger-powered edge detector surpasses trained rivals","No training: quantum-inspired method claims edge-detection crown","Lightweight edge detector bests deep learners on four datasets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000201,"raw_usage":{"total_tokens":1389,"prompt_tokens":967,"completion_tokens":422,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":343}},"tokens_in":583,"tokens_out":422,"duration_ms":30914,"temperature":1.0,"reasoning_tokens":343,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T21:55:55.269416+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-implement the pipeline exactly as Eqs. (3)–(22) specify, run it on a sample of NYUD, BSD500, Multicue, and PASCAL images, and evaluate the raw $E_{\\mathrm{hybrid}}$ map with the standard BSDS benchmark code; if the computed ODS/OIS/AP scores fall materially below the tables, or if the evaluation cannot handle the many tied values introduced by the binary Canny component, the central claim is refuted.","supporting_citations":[{"cited_title":"Holistically-nested edge detection,","cited_arxiv_id":null,"evidence_quote":"Provides the HED deep-learning baseline and the evaluation convention the paper uses for ODS/OIS/AP/F-measure comparisons."},{"cited_title":"Contour detection and hierarchical image segmentation,","cited_arxiv_id":null,"evidence_quote":"Supplies the BSD500 dataset and the gPb-ucm contour-detection baseline used in Tables I and II."},{"cited_title":"Indoor segmentation and support inference from rgbd images,","cited_arxiv_id":null,"evidence_quote":"Supplies the NYUD dataset used in Table I."},{"cited_title":"Edter: Edge detection with transformer,","cited_arxiv_id":null,"evidence_quote":"The transformer-based EDTER detector is the strongest baseline the paper claims to surpass on NYUD, BSD500, and Multicue."},{"cited_title":"Richer convolutional features for edge detection,","cited_arxiv_id":null,"evidence_quote":"The RCF detector appears in all four comparison tables and anchors the claimed improvements over deep edge detectors."},{"cited_title":"A computational approach to edge detection,","cited_arxiv_id":null,"evidence_quote":"Defines the Canny edge-detection algorithm and its thresholding protocol used in the hybrid fusion stage."},{"cited_title":"Dense extreme inception network: Towards a robust cnn model for edge detection,","cited_arxiv_id":null,"evidence_quote":"Supplies the BIPED dataset used for the ablation studies and qualitative comparison."}],"review_version":1}