{"id":"0f5a79fa-d7fe-4a25-8817-dd3e821b7910","arxiv_id":"2506.04664","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A new unsupervised polygonal approximation algorithm that combines bidirectional length-scanning, iterative vertex insertion, merging, and vertex adjustment is reported to be faster than an existing method with comparable quality on MPEG7 shapes.","lead":"This paper introduces a four-phase unsupervised algorithm for replacing digital shape outlines with simpler polygons. The authors report it runs faster than a state-of-the-art method while keeping similar visual quality, but the evidence rests on a single baseline and a self-cited quality metric.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Competitiveness rests on an unvalidated approximate Rosin oracle from the author's own prior work; if that surrogate is biased, the central quality claim is unsupported.","rationale":"The reader identified the same load-bearing assumption: the approximate optimal scheme from the author's prior work is not validated, and the Rosin comparison inherits whatever bias that surrogate has. This is the most serious concern because the paper's only quantitative quality evidence is Figure 5. The speed claim is also weakly supported - the reported 'factor of 1.22 in 10Log10 scale' is ambiguous and no measurement details are given - but that is a secondary issue that could be clarified with a table of timings. The internal algorithm steps are plausible and the claimed complexity O(m'n) is coherent; the weak point is evaluation, not construction. Thus the concern does not change the conditional verdict: the paper should not be rejected outright, but the core empirical claim needs support from an exact or independently validated optimal oracle, ideally with error bars or at least a table of numerical Rosin values.","tokens_in":10346,"tokens_out":4374,"duration_ms":54284,"concrete_test":"Recompute Rosin's measure for the proposed scheme and for Madrid-Cuevas et al. on a subsample of the MPEG7 shapes (e.g., 20 curves spanning the range of vertex counts) using the exact Perez-Vidal optimal scheme [7], and compare those values with the approximate-[23] values used in Figure 5. If the per-curve Rosin values differ by more than a few points, or if the ordering or the reported 'competitive' conclusion changes, then the central quality claim is not supported. Report whether discrepancies correlate with vertex count.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of being 'competitive with Rosin's measure' depends entirely on the Rosin values in Figure 5. Section V states that 'the computational complexity of Perez and Vidal is significantly high, which is why an approximate version of the scheme [23] is used here.' This approximate optimal scheme is cited to the author's own prior work and is not described, its approximation error is not bounded, and no validation is provided against the exact Perez-Vidal algorithm. Rosin's measure is defined relative to an optimal polygon; if the surrogate systematically under-estimates the optimal error for the vertex counts returned by the Madrid-Cuevas et al. baseline, or over-estimates it for the proposed scheme, the claimed competitiveness could be an artifact of the oracle. The paper even notes that Rosin's measure is biased toward larger vertex counts, and since the proposed scheme typically produces fewer vertices, small changes in the optimal-error estimate can flip the comparison. No other quantitative quality metric is reported, so this surrogate is the sole quantitative pillar of the competitiveness claim. Exact computational cost is not a justification for using an unvalidated approximation when the whole experiment is meant to assess quality.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an unsupervised polygonal approximation scheme for closed digital curves, consisting of initial segmentation by bidirectional scanning, iterative vertex insertion, iterative merging, and vertex adjustment. The central claims are that the scheme is faster than state-of-the-art methods and competitive with the Madrid-Cuevas et al. scheme in terms of Rosin's measure and aesthetic quality, with an overall computational complexity of O(m'n). Validation is performed on MPEG7 shapes using visual overlays, Rosin's measure, execution time, and compactness-based robustness under rotation and scaling.","tokens_in":10586,"tokens_out":5459,"duration_ms":67360,"significance":"If the claims are properly supported, the paper offers a simple, unsupervised heuristic with modest complexity and visually plausible output, and the large MPEG7 visual comparison is a useful asset. However, the evidence for the two headline claims is currently thin: only one baseline is used, the Rosin measure is computed with an unvalidated approximate oracle from the author's own prior work, execution-time results are reported without statistical support, and the timing summary is ambiguous. The robustness analysis is a positive addition. The contribution is potentially publishable after the evaluation is substantially strengthened.","major_comments":[{"comment":"The central quality claim, 'competitive with Rosin's measure,' rests entirely on Figure 5, but the Rosin values are computed using an approximate version of Perez and Vidal's optimal scheme taken from the author's prior work [23]. This approximate oracle is not described, no error bound is given, and it is not validated against the exact optimal algorithm. Since Rosin's measure compares each scheme against the optimal polygon for the same vertex count, a biased surrogate could systematically favor one scheme; the paper itself notes that Rosin's measure favors larger vertex counts and that Madrid-Cuevas et al. generally produce more vertices. The authors should compute Rosin's measure with the exact Perez-Vidal algorithm on at least a representative subset of curves, or validate the approximation against exact optimal values and report the maximum and mean absolute error. Without this, Figure 5 does not support the competitiveness claim.","section":"Section V, Figure 5 and Section III"},{"comment":"The execution-time comparison uses a single baseline and reports that the Madrid-Cuevas et al. scheme is 'on average slower than the proposed scheme by a factor of 1.22 in 10Log10 scale.' This sentence is ambiguous: if 1.22 is the average difference in 10*log10(time), the geometric-mean ratio is about 1.32, whereas if it is a difference in log10(time) the ratio is implausibly large. No standard deviations, confidence intervals, or per-curve statistics are given, and the line diagram alone cannot establish a general speed advantage. The authors should define the scale precisely, report the distribution of timings (e.g., median and interquartile range over multiple runs), and include a statistical test such as the Wilcoxon signed-rank test over the MPEG7 set.","section":"Section V, Figure 6"},{"comment":"The abstract and conclusion claim superiority or competitiveness with 'state-of-the-art' approaches, but the paper compares only with Madrid-Cuevas et al. [5]. A single baseline cannot support a state-of-the-art claim. At least one or two additional recent unsupervised schemes, such as Carmona-Poyato et al. [15], Fernandez-Garcia et al. [18], or Parvez [20], should be included. In addition, Rosin's measure is the only quantitative quality metric; the authors should also report other measures such as the figure of merit or the compression ratio versus approximation error, and perform a statistical comparison across the dataset.","section":"Section V, Table I and Figures 5-7"},{"comment":"The stopping criterion for vertex insertion is the heuristic m + E2, and the text states that using the second or third power of m caused over-smoothing. This makes the exponent an empirically selected free parameter, and no sensitivity analysis is provided. Because this heuristic determines the final vertex count and therefore affects all downstream quality comparisons, the authors should either justify the choice analytically or report how the results vary with the exponent (e.g., m, m^2, m^3) on a few representative curves. Without this, the 'unsupervised' claim is tied to a hand-fitted criterion rather than to a principled stopping rule.","section":"Section IV, iterative vertex insertion"}],"minor_comments":[{"comment":"Step 5 says 'Repeat Step 4 and 5 until the approximation is stabilized,' which is self-referential; it should refer to Steps 3 and 4 (merging and vertex adjustment).","section":"Algorithm, Step 5"},{"comment":"The text says the scheme comprises 'three phases' but then lists four: initial segmentation, iterative vertex insertion, iterative merging, and vertex adjustment. Please correct the number or the list.","section":"Abstract and Section IV"},{"comment":"The name 'Pervez and Mauhmud [19]' should be 'Parvez and Mahmoud'; also, 'Perez' in reference [7] is a different author, so the spelling should be checked throughout.","section":"Section II and References"},{"comment":"The definition of Rosin's measure is garbled: the sentence beginning 'Fidelity is defined by the ratio...' mixes fidelity and efficiency and should be rewritten for clarity.","section":"Section III"},{"comment":"The table lists 'Cup' twice, and the row header 'Horsesho e' contains a line-break error; also, several rows appear to be missing or misaligned in the text version.","section":"Table I"},{"comment":"Figures 5, 6, and 7 are referenced but not actually embedded in the manuscript text provided; the published version must include legible figures with axis labels, legends, and a clear statement of the curve ordering on the horizontal axis.","section":"Figures 5-7"},{"comment":"The 'coefficient of variation (scaled)' in Figure 7 is not defined; please state the scaling and how compactness is computed for polygons with different vertex counts.","section":"Section V, robustness"},{"comment":"The overall complexity O(m'n) does not account for the outer loop that repeats merging and vertex adjustment until stabilization; either bound the number of iterations by a constant or include it in the complexity expression.","section":"Section IV, complexity"}],"recommendation":"major_revision","confidential_remarks":"The evaluation of the paper's central quality claim depends on an approximate version of Perez and Vidal's optimal scheme taken from the author's own prior work [23]. This is not a matter of misconduct, but the manuscript must make that oracle independently checkable, either by describing it in sufficient detail or by providing validation against the exact algorithm. The editor may also wish to consider whether a single-baseline comparison is sufficient for a journal-level claim of state-of-the-art performance; the comparison set can be broadened without changing the paper's core contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The algorithm itself is the best part of this paper. It is clearly described, the complexity claims look sensible, and the combination of bidirectional length-decrease scanning, iterative vertex insertion, merging with a safety check, and strongest-vertex-first adjustment is a new assembly even if each component has precedents. The visual results on MPEG7 shapes are plausible and the method does seem to produce aesthetically reasonable approximations with fewer vertices than the Madrid-Cuevas et al. baseline. That is a real, if incremental, contribution to a mature subfield.\n\nThe soft spot is exactly where the stress-test note lands. The competitiveness claim on Rosin's measure depends entirely on Figure 5, and that figure is computed using an \"approximate version\" of Perez-Vidal's optimal scheme taken from the author's own 2021 paper [23]. The approximation is not described, its error is not bounded, and it is not validated against the exact scheme anywhere in the text. The paper even acknowledges that Rosin's measure is biased toward larger vertex counts, and the proposed method typically produces fewer vertices than the baseline. That means small systematic changes in the estimated optimal error could flip the comparison. This is not a hidden flaw; Section V states it openly, but openness does not make the evaluation sound. The speed comparison is also reported poorly: saying the baseline is slower \"by a factor of 1.22 in 10Log10 scale\" is just ambiguous.\n\nOther weaknesses are real but less severe. There is only one baseline, no error bars or statistical tests, no code, and the vertex-insertion heuristic (m + E2) was hand-fitted after trying second and third powers of vertex count. That is acceptable for a heuristic paper but it should be stated more explicitly.\n\nFor whom is this paper? Someone working on polygonal approximation or on speeding up shape-based pipelines might find it useful. A reader looking for a rigorous comparative evaluation would be disappointed.\n\nMy recommendation: send it to peer review, but with the clear expectation of major revision. The algorithm deserves a careful look, but the authors need to validate or replace the approximate optimal scheme, add at least one more baseline, report statistics, and clarify the runtime claim. Without those changes, the central claim of \"competitive with Rosin's measure\" is not supported.","headline":"A plausible incremental algorithm whose main empirical claim is undercut by an unvalidated Rosin oracle from the author's own prior work.","tokens_in":11054,"tokens_out":1205,"would_cite":false,"duration_ms":16986,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68U05","68T10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Fast unsupervised scheme rivals top polygon-fit quality","keywords":["polygonal approximation","unsupervised","digital curve","vertex insertion","vertex merging","vertex adjustment","Rosin's measure","MPEG7"],"falsifier":"Recompute Rosin's measure for the MPEG7 curves using an exact optimal polygonal approximation, such as dynamic programming for the min-# or min-ε problem, for the vertex counts and errors produced by both schemes; if the proposed scheme's merit, or its ranking against the comparison scheme, changes materially, the competitiveness claim fails.","tokens_in":10111,"feed_emoji":"📐","tokens_out":5878,"duration_ms":62239,"temperature":0.7,"pith_summary":"This paper claims a fast, unsupervised algorithm that approximates a closed digital curve by a polygon without requiring the user to set a vertex count or error threshold. The scheme first finds sharp corners by scanning the curve and watching for the scanning chord to shrink, then greedily inserts vertices where error is largest, merges away weak vertices, and adjusts the remaining vertices to reduce squared error. On the MPEG7 shape dataset the approximations look almost identical to those of a leading unsupervised method, run faster in every reported test, and are competitive under Rosin's fidelity-efficiency measure. If the claim holds, polygonal approximation becomes a cheaper preprocessing step for shape representation, recognition, and compression.","feed_headline":"Fast unsupervised scheme rivals top polygon-fit quality","feed_subtitle":"Three-phase scan-and-merge cuts runtime while matching Rosin's measure on MPEG7 curves.","key_machinery":"The load-bearing mechanism is the sharp-turn detector: while a scanning segment endpoint moves along the curve, if the Euclidean distance from the fixed start to the endpoint decreases instead of increasing, the curve point just passed is marked as a probable vertex. This cheap test, run clockwise and counterclockwise, generates the initial segmentation in O(n). The rest of the pipeline, iterative vertex insertion using a stopping heuristic of vertex count plus squared error, weakest-vertex merging with a self-intersection guard, and strongest-vertex adjustment, refines this set while keeping the total complexity O(m'n).","core_discovery":"The paper's central claim is that high-quality polygonal approximation can be obtained by combining an O(n) scan for sharp turns with iterative vertex insertion, iterative merging, and vertex adjustment, at overall complexity O(m'n). The paper reports that on the MPEG7 curves this scheme is faster than the comparison unsupervised scheme, is competitive under Rosin's measure, which is the geometric mean of fidelity and efficiency relative to an optimal polygon, and is more robust to rotation and scaling as measured by the coefficient of variation of compactness. The supporting evidence is the visual similarity of the overlaid polygons, the Rosin merit plot, and the execution-time plot.","pith_inferences":["The scanning-chord contraction test is a discrete proxy for curvature extrema and could be adapted to open curves or to multi-scale analysis by varying the chord-length threshold.","The stopping heuristic, number of vertices plus squared error, is essentially a penalized-error criterion; formalizing the penalty could yield a principled model-selection rule.","Because Rosin's measure in the paper uses an approximate optimal scheme from the author's earlier work, an exact optimal comparison on small curves would test whether the competitiveness claim is robust.","The self-intersection guard in the merging phase suggests the scheme may extend to noisy or self-approaching curves if the error threshold is estimated adaptively."],"forward_implications":["Users get a scale-free approximation: no vertex-count or error threshold needs to be supplied.","Because the initial scan is O(n) and the total cost is O(m'n), the scheme is practical for long digital boundaries.","The reported average runtime gap of 1.22 units on a 10Log10 scale places the scheme faster than the comparison method across the MPEG7 test set.","Sharp corners are retained faithfully, which benefits object recognition, character recognition, and signature verification.","Stable compactness under rotation and scaling suggests the approximation is suitable for invariant shape matching."],"supporting_citations":[{"why":"Supplies the unsupervised scheme that serves as the baseline for aesthetics, Rosin's measure, runtime, and robustness.","marker":"[5]"},{"why":"Supplies the optimal-reference polygon used in Rosin's measure.","marker":"[7]"},{"why":"Defines the fidelity-efficiency measure used for quality comparison.","marker":"[8]"},{"why":"Provides the sequential scanning idea behind the sharp-turn detector.","marker":"[10]"},{"why":"Used to justify the self-intersection guard in the merging phase.","marker":"[19]"},{"why":"Provides the MPEG7 shape dataset used for all experiments.","marker":"[22]"},{"why":"Supplies the approximate version of the optimal scheme used to compute Rosin's measure.","marker":"[23]"}],"fun_headline_variants":["Unsupervised polygonal fit matches Rosin's quality, faster","Fast unsupervised polygon method rivals Rosin-based metrics","Three-phase scan-and-merge speeds polygonal approximation","Robust polygonal approximation via iterative vertex insertion","Rotation-robust polygonal fit, unsupervised and fast"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The competitiveness evidence depends on the approximate optimal scheme used to compute Rosin's measure being accurate enough; if that approximation is biased, the reported Rosin comparisons may not reflect true fidelity and efficiency.","fun_headline_variants_meta":{"raw":{"variants":["Unsupervised polygonal fit matches Rosin's quality, faster","Fast unsupervised polygon method rivals Rosin-based metrics","Three-phase scan-and-merge speeds polygonal approximation","Robust polygonal approximation via iterative vertex insertion","Rotation-robust polygonal fit, unsupervised and fast"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00057,"raw_usage":{"total_tokens":2636,"prompt_tokens":825,"completion_tokens":1811,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":441,"completion_tokens_details":{"reasoning_tokens":1733}},"tokens_in":441,"tokens_out":1811,"duration_ms":16365,"temperature":1.0,"reasoning_tokens":1733,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:35:37.619312+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute Rosin's measure for the MPEG7 curves using an exact optimal polygonal approximation, such as dynamic programming for the min-# or min-ε problem, for the vertex counts and errors produced by both schemes; if the proposed scheme's merit, or its ranking against the comparison scheme, changes materially, the competitiveness claim fails.","supporting_citations":[{"cited_title":"An efficient unsupervised method for obtaining polygonal approximations of closed digital planar curves","cited_arxiv_id":null,"evidence_quote":"Supplies the unsupervised scheme that serves as the baseline for aesthetics, Rosin's measure, runtime, and robustness."},{"cited_title":"Optimum polygonal approximation of digitized curves","cited_arxiv_id":null,"evidence_quote":"Supplies the optimal-reference polygon used in Rosin's measure."},{"cited_title":"Techniques for assessing polygonal approximations of curves","cited_arxiv_id":null,"evidence_quote":"Defines the fidelity-efficiency measure used for quality comparison."},{"cited_title":"A fast sequential method for polygonal approximation of digitized curves","cited_arxiv_id":null,"evidence_quote":"Provides the sequential scanning idea behind the sharp-turn detector."},{"cited_title":"Polygonal approximation of digita l planar curves through adaptive optimizations","cited_arxiv_id":null,"evidence_quote":"Used to justify the self-intersection guard in the merging phase."},{"cited_title":"Some algorithms under non -parametric framework versus an unsupervised approach","cited_arxiv_id":null,"evidence_quote":"Supplies the approximate version of the optimal scheme used to compute Rosin's measure."}],"review_version":1}