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REVIEW 6 major objections 6 minor 50 references

A Hybrid Framework for Blood Vessel Morphology Classification: Discrete Geometry-based Tortuosity Feature Measurement, Information Gain-based Feature Selection, and Random Forest Classification

T0 review · 6 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Six curvature and torsion features, selected by information gain, let a random forest reproduce physician tortuosity grades (Macro-F1 0.92 binary, 0.86 ternary).

desk verdict A competent feature-selection-and-classification study whose headline F1s are probably a bit inflated because the six features were chosen on the full dataset before cross-validation; fixable, and worth a referee. read the letter →

arxiv 2607.14195 v1 pith:2OOYGR6J submitted 2026-07-15 eess.IV

Yu Zhong , Jingzhi Guo , Luyao Li , Zehao Wang , Zhihui Yang , Yixin Lin , Weilun Fu , Yang Wang This is my paper
classification eess.IV
keywords bloodvesseltortuosityinternalcarotidarterydiscretegeometrycurvatureandtorsionfeatureselectioninformationgainrandomforestmorphologicalriskindex
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

Physicians grade ICA-C1 vessel tortuosity visually, which is experience-dependent, and the standard Tortuosity Index (L/D) cannot distinguish in-plane bending from out-of-plane twisting. This paper attempts to establish that a reproducible, geometry-only substitute exists: on 379 clinical centerlines, it computes pointwise curvature and torsion with a discrete derivative estimator, aggregates them into 13 features, prunes to six non-redundant ones via Information Gain and Spearman correlation, and trains a Random Forest. The reported Macro-F1 is 0.9206 for binary severe/non-severe screening and 0.8626 for ternary straight/low/high grading, with a Morphological Risk Index summarizing the model's feature importances. If the pattern holds, clinicians could obtain an objective numerical tortuosity readout that supports both coarse screening and finer morphological distinctions.

What carries the argument

The central mechanism is a discrete-geometry derivative estimator: at each centerline point, a constrained least-squares fit (via Lagrange multipliers) over a sliding window yields stable first, second, and third derivatives r', r'', r'''; these feed the standard Frenet formulas for curvature κ(t) and torsion τ(t). Aggregating these per-point values produces 13 global, averaged, and length-normalized features. A two-stage filter—Information Gain ranking followed by Spearman correlation pruning (|ρ|>0.95)—removes redundant/low-ranked features, yielding the six-feature set. The Random Forest classifier maps these six features to labels, with cost-sensitive class weights to handle imbalance and

What would settle it

Have independent neuroradiologists re-grade the same 379 centerlines and measure inter-rater agreement (e.g., Cohen's kappa); then test the trained six-feature model on a multi-center external dataset. If kappa is far below the model's Macro-F1, or if Macro-F1 drops substantially on the external data, the model is encoding a single rater's or single center's idiosyncrasies rather than a generalizable morphological rule.

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Extended reading notes

Core claim

The authors aim to establish that a distance-based metric like the Tortuosity Index is geometrically ambiguous (a Salkowski curve and a helix can share identical L/D values) and that a compact set of curvature- and torsion-derived features can replace subjective visual grading. From 379 ICA-C1 centerlines, they estimate pointwise curvature and torsion via a sliding-window least-squares derivative method, build 13 aggregate features, prune to six (TI, AC, TC, AC/AT, AT, TT) by Information Gain and Spearman correlation, and train a Random Forest. Reported nested out-of-fold Macro-F1 is 0.9206 for binary severe/non-severe screening and 0.8626 for ternary straight/low/high grading. Ablation show

Load-bearing premise

The reported scores are computed against the physicians' previous visual morphological classification, so if those ratings are inconsistent or rater-dependent, the model is matching a subjective reference rather than an objective geometric ground truth.

Editorial extensions

If this is right

  • If the reported performance generalizes, tortuosity assessment could become an automated, reproducible measurement rather than a subjective visual judgment.
  • The six-feature set is small enough to be checked by hand after centerline extraction, making it a practical candidate for integration into CTA reading workflows.
  • The ablation result implies that a fast binary screen only needs three curvature features (TI, AC, TC), while torsion features become necessary when grading into three morphological classes.
  • The Morphological Risk Index provides a single numeric summary that could be tracked over time or compared across patients, though the paper explicitly frames it as exploratory.
  • Because the labels come from a physician's prior visual classification, the framework should be read as quantifying that clinical consensus, not as discovering an independent ground truth.

Reading between the lines

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

  • A natural extension is to apply the same discrete-geometry feature pipeline to other vessels (e.g., coronary or cerebral arteries) and retrain the classifier, since the mathematics does not depend on the carotid anatomy.
  • A multi-reader agreement study would clarify whether the model is learning a stable morphological signal or encoding one rater's idiosyncrasies; if model F1 exceeds human-human agreement, the model could serve as a reference standard.
  • The phantom-based argument (identical TI for Salkowski and helix) suggests any proposed replacement metric should be tested against a library of such geometric-ambiguity pairs before being adopted for clinical use.
  • The MRI thresholds are sample-based and require external validation; a concrete next test would be to correlate MRI with procedural outcomes such as catheter navigation time or first-pass recanalization.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

6 major / 6 minor

Summary. This paper proposes a hybrid framework for classifying ICA-C1 vascular tortuosity using 379 clinical centerlines (193 subjects). Thirteen geometric features are computed from centerlines by discrete least-squares derivative estimation (curvature, torsion, integrals), and a cascade of information-gain ranking and Spearman correlation pruning reduces them to six features (TI, AC, TC, AC/AT, AT, TT). A random forest is compared with LR, SVM, and XGBoost under nested 5-fold cross-validation; the authors report Macro-F1 0.9206 for binary severe/non-severe screening and 0.8626 for ternary straight/low/high grading. A Morphological Risk Index (MRI) is defined from RF impurity importances with thresholds set at midpoints of group means. The paper also illustrates the insufficiency of TI with matched phantom curves.

Significance. The geometric feature set and the phantom demonstration in Section II-B are useful and clearly presented; the ablation and model comparisons are appropriate in spirit, and the authors explicitly label the MRI as exploratory and list limitations. If the evaluation protocol were corrected (feature selection nested inside CV, subject-level grouping, uncertainty quantification), the central claim of high Macro-F1 would be a meaningful, reproducible contribution to objective tortuosity grading. At present, however, the headline numbers are not trustworthy because of selection bias and unaccounted data dependence.

major comments (6)
  1. [IV-A / III-D-2] The IG ranking and Spearman pruning are computed once on the full labeled dataset before the nested cross-validation. Thus the outer-fold test labels participate in choosing the six-feature subset, so the 'out-of-fold' predictions are not independent of the test labels. With 379 samples and highly correlated features, this selection bias tends to inflate Macro-F1. Please move the entire feature-selection cascade inside each outer training fold and report selection stability, or justify why the bias is negligible.
  2. [III-A / III-D-2] The data are 379 vessels from 193 subjects. Vessel-level k-fold splitting can place the two vessels of one subject in both training and test, inflating generalisation. Report subject-level grouped cross-validation or a mixed-effects/random-intercept analysis.
  3. [Tables IV, VI, VIII] Only point estimates are given. The difference RF vs XGBoost in binary is 0.0009, and the ablation differences are less than 0.01; without foldwise standard deviations, confidence intervals, or paired tests these differences are uninterpretable. Add fold-level results and CIs.
  4. [Table VII] The ternary confusion matrices sum to 93, 112, and 174 for Straight, Low, and High rows, while Table III gives group sizes N=93, 174, 112. The row/sample-size labeling is therefore inconsistent. The text's comparison of high-tortuosity misclassifications (RF 15 vs LR/SVM 31) relies on these rows; correct the table and recompute the error counts.
  5. [Eqs. (28)-(29)] MRI thresholds are midpoints of full-sample group means and are not evaluated on held-out data. These are in-sample fitted decision rules; as published they are not validated reference ranges. Please report cross-validated or external performance of the MRI thresholds, or explicitly state that they are descriptive full-sample statistics with no decision-making claim.
  6. [III-A / IV-A] The binary label definition is not stated. The text says binary and ternary labels are not a one-to-one mapping, yet the Table V class sizes (267/112) coincide with merging 'straight'+'low' vs 'high'. Specify how 'severe' was derived, and report the annotation protocol and inter-rater reliability for the physician's ternary grades used as labels.
minor comments (6)
  1. [III-D-2] The text mentions an 'inner 3-fold loop' for hyperparameter search but later says '5-fold nested OOF'; clarify the number of inner folds and report grid ranges.
  2. [IV-C-1] 'Fig. V' should be 'Table V'.
  3. [III-C-1] The number of quantile bins K for IG discretization is not given; without it the IG ranking is not reproducible.
  4. [III-D-3] The ablation tolerance ('10^-3 scale') is not defined; specify how the tolerance interval was set.
  5. [Methods] Consider reporting data/code availability and the exact RF hyperparameters (number of trees, max depth, class weights) to make the experiments reproducible.
  6. [Table VIII] The 'peaks' at 3 and 5 features are within 0.01 of the 6-feature baseline, but without variance estimates the statement that these are 'equivalent' is not supported.

Circularity Check

2 steps flagged · score 6.0 of 10

Full-data IG feature selection and MRI thresholds fitted to the same labels make several reported results partially circular.

  1. fitted input called prediction [Section III-D-2 with feature selection in Section IV-A / III-C]
    "First, we calculated IG values based on the physician’s previous ternary morphological classification ... The optimal models were subsequently evaluated solely on the mutually exclusive outer test folds ... ensuring an unbiased mathematical estimation of the model’s empirical risk on unseen geometric data."

    The six-feature subset (TI, AC, TC, AC/AT, AT, TT) is selected once by Information Gain and Spearman correlation using all 379 labeled vessels before the nested 5-fold CV is run. Thus the labels in the outer test folds have already influenced which features enter the RF. The OOF predictions are not generated by a model whose input representation was fixed without access to the test labels; the reported Macro-F1 values (0.9206 and 0.8626) are therefore not fully out-of-sample estimates. This is a circular validation step, not a pure prediction on unseen data.

  2. fitted input called prediction [Section IV.C.4, Eqs. (28)-(29)]
    "Here, the mean MRI scores are −0.4003 for the non-severe group and 0.9542 for the severe group, yielding θ0 =(−0.4003+0.9542)/2=0.2770."

    The MRI classification thresholds are defined as the midpoints of the observed group means of the MRI scores computed on the very same labeled data. Equations (28) and (29) then assign each vessel to the side of these fitted thresholds. Consequently, the group means are guaranteed to fall on their respective sides of the threshold by construction; any separation of the group means is an arithmetic consequence of the definition rather than an independent predictive finding. The paper labels the MRI exploratory, but the threshold-based categorization is still a fitted rule, not a validated prediction.

full rationale

The geometric feature measurement chain is self-contained: curvature, torsion, TI, AC, TC, AT, TT, and AC/AT are computed from centerline coordinates using standard discrete differential geometry formulas and do not use the labels. There are no load-bearing self-citations and no uniqueness theorem imported from the authors. The RF classifier itself is a standard algorithm. However, two steps close the loop. First, the feature selection by Information Gain uses the physician ternary labels over the full dataset before the outer cross-validation folds are formed, so the headline OOF Macro-F1 estimates are affected by label leakage and are not strictly independent predictions. Second, the MRI thresholds in Eqs. (28)-(29) are midpoints of group means from the same data, making the reported group separation tautological. These are fitted inputs presented as predictive outputs, so the paper is partially circular even though the underlying geometric derivations are not. The paper's own limitations section acknowledges the need for external validation, which mitigates but does not remove the circular construction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The framework pulls standard differential geometry and ML machinery from the literature; the paper's own contribution is the feature set selection and MRI, both of which are fit on the same 379-vessel dataset.

free parameters (6)
  • Derivative window radii m=(1,1,1)
    Chosen without sensitivity analysis; directly controls curvature/torsion estimates.
  • Gaussian smoothing sigma = 1
    Applied to centerline coordinates; choice affects derivative noise.
  • IG quantile binning = not specified
    Information Gain requires discretizing continuous features; bin count is not reported.
  • Spearman correlation threshold = 0.95
    Features with |rho|>0.95 pruned; threshold chosen by hand.
  • MRI thresholds theta0, theta1, theta2 = 0.2770, -0.4555, 0.3527
    Midpoints of group mean MRI scores on the same dataset; fitted, not validated.
  • Ablation tolerance = 1e-3
    Performance differences below 1e-3 treated as equivalent; chosen post hoc.
assumptions (5)
  • standard math The Frenet frame is well-defined: centerline is smooth with nonzero curvature at sample points.
    Used in Section II-A to define curvature and torsion via Eqs. (2)-(3).
  • domain assumption The centerline extraction and smoothing pipeline produces a faithful discrete representation of the vessel centerline.
    Section III-A; accuracy of all features depends on this.
  • domain assumption Physician visual grading provides reliable ground-truth morphological labels.
    Section IV-A; labels are the target for IG ranking and classification.
  • domain assumption ICA-C1 segment identification via multi-planar visualization is anatomically correct.
    Section III-A1-2.
  • domain assumption The discrete least-squares derivative estimator with m=(1,1,1) accurately approximates true derivatives at ~0.994 points/mm sampling.
    Section III-B1; no convergence or bias analysis is provided.
invented entities (1)
  • Morphological Risk Index (MRI)
    purpose: Provide a single numerical score summarizing vessel morphology from RF feature importances, with thresholds for binary/ternary categories.
    The weights are derived from the fitted RF on the same dataset and thresholds are midpoints of training group means; no external validation or prospective prediction is provided.

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Cite this review

Pith. "Pith review of A Hybrid Framework for Blood Vessel Morphology Classification: Discrete Geometry-based Tortuosity Feature Measurement, Information Gain-based Feature Selection, and Random Forest Classification." pith.science (2026). https://pith.science/paper/2OOYGR6J

@misc{pith2026260714195,
  author       = {Pith},
  title        = {Pith review of: A Hybrid Framework for Blood Vessel Morphology Classification: Discrete Geometry-based Tortuosity Feature Measurement, Information Gain-based Feature Selection, and Random Forest Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2OOYGR6J}},
  note         = {Machine review of arXiv:2607.14195}
}
abstract

Subjective visual grading of blood vessel tortuosity relies heavily on clinical experience, while traditional distance-based indices often fail to adequately characterize three-dimensional spatial deformation. Because abnormal internal carotid artery morphology may be clinically relevant to cerebrovascular assessment and stroke-risk evaluation, objective and reproducible quantification of vascular tortuosity is of considerable importance. To address this limitation, we propose a mathematical framework for the morphological classification of the internal carotid artery (ICA-C1) segment. The framework integrates discrete geometric feature measurement, Information Gain-based feature selection, and Random Forest classification. An initial set of 13 tortuosity features is extracted from the corresponding 379 clinical vascular centerlines using discrete geometric methods and subsequently reduced to a six-feature subset consisting of $\mathcal{TI}$, $\mathcal{AC}$, $\mathcal{TC}$, $\mathcal{AC}/\mathcal{AT}$, $\mathcal{AT}$, and $\mathcal{TT}$. The framework is evaluated in two classification tasks. For binary classification of non-severe and severe tortuosity, the RF model achieves a Macro-F1 score of 0.9206. For ternary morphological grading into straight, low-tortuosity, and high-tortuosity groups, it achieves a Macro-F1 score of 0.8626. The results indicate that elongation- and curvature-related features provide strong discriminatory information for basic screening, whereas torsion-related features contribute additional information for more detailed morphological classification. Based on the RF feature-importance values, we further define a Morphological Risk Index (MRI), which provides a direct numerical reference for vascular morphology and may facilitate more objective and consistent clinical assessment.

Figures

Figures reproduced from arXiv: 2607.14195 by the authors.

Figure 1
Figure 1. Traditional clinical qualitative classification of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The proposed geometry-driven dual-task classi [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Schematic representation of intrinsic geometric [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: (a) Blood Vessel Phantoms: A Salkowski vascular phantom and a standard helix phantom yield an iden￾tical Tortuosity Index (T I) of 1.9877. (b) Real clinical ICA-C1 segments: Four comparative groups of patient vessels, where the two vessels within each group exhibit ent…
Figure 5
Figure 5. Figure 5: The overall mathematical framework and operational pipeline of the proposed method. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Three views from Mimics medical imaging software, showing the anatomical location and morphology of the [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Pipeline of vascular reconstruction and centerline extraction. (a) Raw vessel model with segmentation noise. [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 8
Figure 8. Figure 8: Sliding-window least-squares estimation of [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: The overall flowchart of the proposed data-driven hybrid framework. The upper row illustrates the [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Information Gain ranking of the extracted blood [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: Spearman rank correlation matrix of the ex [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: Boxplots of the six retained features across the three classes. [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

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Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.