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arxiv: 2605.28176 · v1 · pith:GLJJL7DXnew · submitted 2026-05-27 · 💻 cs.CV

From Kellgren-Lawrence to Calcium Pyrophosphate Crystal Deposition: A Soft-Labelling Framework for Knee Osteoarthritis Assessmen

Francisco B\'erchez-Moreno , Riccardo Rosati , Maria Chiara Fiorentino , V\'ictor M. Vargas , Edoardo Cipolletta , Emilio Filippucci , Luca Romeo , Pedro A. Guti\'errez
show 1 more author
C\'esar Herv\'as-Mart\'inez
This is my paper

Pith reviewed 2026-06-29 13:07 UTC · model grok-4.3

classification 💻 cs.CV
keywords knee osteoarthritissoft labellingdeep learningX-ray gradingKellgren-LawrenceCPPDordinal classificationmedical imaging
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0 comments X

The pith

Soft-labelling with unimodal distributions improves ordinal grading of knee osteoarthritis on X-rays over one-hot labels.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an ordinal deep learning framework that replaces one-hot labels with soft unimodal probability distributions for grading knee X-rays on both the Kellgren-Lawrence and CPPD scales. It tests four formulations—binomial, beta, triangular, and exponential—on a dataset of 2172 images including 968 jointly annotated for both tasks. All strategies outperformed the conventional one-hot baseline, with the triangular formulation reaching the highest QWK of 0.796 and lowest MAE of 0.438 on CPPD grading, and the beta formulation reaching QWK of 0.777 and MAE of 0.529 on KL grading. A sympathetic reader would care because this addresses the mismatch between standard classification losses and the ordinal, uncertain nature of clinical severity scores while respecting the observed asymmetry between the two scales.

Core claim

The central claim is that an ordinal DL framework based on soft-labelling, replacing one-hot targets with unimodal probability distributions centred on the annotated grade, consistently outperforms nominal one-hot supervision for both KL and CPPD grading tasks. Specifically, the triangular formulation achieved the highest QWK and lowest MAE for CPPD (QWK = 0.796; MAE = 0.438), while the beta-based approach provided the best overall performance for KL (QWK = 0.777; MAE = 0.529; AMAE = 0.523; MMAE = 0.775), with all soft-labelling strategies demonstrating statistically significant improvements over the baseline (p < 0.001).

What carries the argument

Soft-labelling via unimodal probability distributions (binomial, beta, triangular, exponential) centred on the annotated grade, used as targets instead of one-hot vectors.

If this is right

  • All four soft-labelling strategies improve Quadratic Weighted Kappa and reduce Mean Absolute Error compared to one-hot labels on both grading tasks.
  • The triangular formulation yields the best overall metrics for CPPD grading.
  • The beta formulation yields the best overall metrics for KL grading, including lowest class-wise errors.
  • The performance gains are statistically significant at p < 0.001 across the 2172-image dataset.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may extend to other ordinal scoring tasks in radiology where annotation uncertainty is high.
  • Joint modelling of KL and CPPD could further exploit the asymmetric clinical relationship if the framework is adapted to multi-task training.
  • If the unimodal assumption holds across datasets, the method could lower sensitivity to inter-rater variability in clinical annotations.

Load-bearing premise

Unimodal probability distributions centred on the annotated grade accurately capture both the ordinal uncertainty of the scores and the asymmetric clinical relationship between the KL and CPPD scales.

What would settle it

A replication study on an independent set of knee X-rays where the soft-labelling models fail to achieve higher QWK or lower MAE than the one-hot baseline would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.28176 by C\'esar Herv\'as-Mart\'inez, Edoardo Cipolletta, Emilio Filippucci, Francisco B\'erchez-Moreno, Luca Romeo, Maria Chiara Fiorentino, Pedro A. Guti\'errez, Riccardo Rosati, V\'ictor M. Vargas.

Figure 1
Figure 1. Figure 1: Knee radiographs illustrating the complexity of jointly assessing Osteoarthritis [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Representative examples of the different Kellgren–Lawrence (KL) and Calcium [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic representation of the proposed ordinal deep learning framework for [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example of the binomial (a), exponential (b), beta (c) and triangular (d) discrete [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Combined violin and box plots of the AMAE distributions for all methodologies. [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Confusion matrices comparing the best-performing soft-labelling models for each [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Grad-CAM visualisations across all severity grades for the nominal baseline and [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Residuals with the difference of the average obtained contingency tables and [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Grad-CAM analysis of model robustness under co-occurring pathologies. The [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
read the original abstract

Background and objective. Conventional Deep Learning (DL) approaches for Knee Osteoarthritis (KOA) grading rely on one-hot labels, which fail to capture both the ordinal uncertainty of Kellgren--Lawrence (KL) and Calcium Pyrophosphate Deposition Disease (CPPD) severity scores and the asymmetric relationship between the two scales observed in clinical practice. Methods. We retrospectively collected 2172 knee X-ray images, including 968 radiographs jointly annotated for KL and CPPD severity. An ordinal DL framework based on soft-labelling was developed for both tasks, replacing one-hot targets with unimodal probability distributions centred on the annotated grade. Four formulations were investigated: binomial, beta, triangular, and exponential. Results. All soft-labelling strategies consistently outperformed the nominal baseline. For CPPD grading, the triangular formulation achieved the highest Quadratic Weighted Kappa (QWK) and the lowest Mean Absolute Error (MAE) (QWK = 0.796; MAE = 0.438), while the beta formulation yielded the most balanced class-wise performance considering Average MAE (AMAE) and Maximum MAE (MMAE) across classes (AMAE = 0.458; MMAE = 0.573). For KL grading, the beta-based approach provided the best overall performance, achieving the highest QWK together with the lowest MAE and class-wise errors (QWK = 0.777; MAE = 0.529; AMAE = 0.523; MMAE = 0.775). Statistical analysis demonstrated significant improvements over conventional one-hot supervision (p < 0.001).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a soft-labelling framework for ordinal grading of knee osteoarthritis on X-rays, replacing one-hot targets with four fixed unimodal distributions (binomial, beta, triangular, exponential) centered on the annotated KL or CPPD grade. Using 2172 images (968 jointly annotated), it reports that all soft-labelling variants outperform the one-hot baseline on QWK and MAE for both tasks, with the triangular distribution best for CPPD (QWK=0.796, MAE=0.438) and beta best for KL (QWK=0.777, MAE=0.529), all with p<0.001.

Significance. If the gains arise from faithful modeling of ordinal uncertainty rather than generic regularization, the approach could improve robustness in medical ordinal classification tasks. The use of jointly annotated cases and multiple distribution families is a positive empirical step, but the heuristic nature of the labels limits claims about capturing clinical asymmetry or uncertainty.

major comments (3)
  1. [Methods] Methods (soft-labelling section): The four distributions are defined with fixed, hand-chosen parameters and applied independently to KL and CPPD; no derivation from inter-rater agreement data, longitudinal progression, or joint KL-CPPD statistics is provided, so the claim that they capture 'ordinal uncertainty' and 'asymmetric relationship' rests on an untested assumption.
  2. [Results] Results and data description: The 968 jointly annotated radiographs are used only for separate per-task training; no joint model, cross-task loss, or analysis of KL-CPPD co-occurrence is presented, leaving the background claim of asymmetry unaddressed by the experiments.
  3. [Results] Evaluation: Performance improvements are reported on QWK/MAE but no ablation compares the chosen unimodal forms against alternatives (e.g., learned label smoothing or empirical inter-rater distributions), so it is unclear whether gains exceed what standard regularization would achieve.
minor comments (2)
  1. [Abstract] Abstract: The statistical test yielding p<0.001 is not named (paired t-test, Wilcoxon, etc.), and the exact data splits or cross-validation scheme are not summarized.
  2. [Methods] Notation: The precise functional forms and parameter values for the beta, triangular, and exponential distributions should be given explicitly (e.g., as equations) rather than described only qualitatively.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, indicating revisions where the manuscript will be updated to clarify claims and strengthen the evaluation.

read point-by-point responses

  1. Referee: [Methods] Methods (soft-labelling section): The four distributions are defined with fixed, hand-chosen parameters and applied independently to KL and CPPD; no derivation from inter-rater agreement data, longitudinal progression, or joint KL-CPPD statistics is provided, so the claim that they capture 'ordinal uncertainty' and 'asymmetric relationship' rests on an untested assumption.

    Authors: We agree that the parameters were selected heuristically based on general ordinal properties rather than derived from inter-rater statistics, longitudinal data, or joint KL-CPPD co-occurrence in this dataset. The claims in the introduction regarding capturing ordinal uncertainty and asymmetry therefore rest on the suitability of unimodal distributions rather than empirical derivation. In the revised manuscript we will qualify these claims in the methods, introduction, and discussion, add a dedicated limitations paragraph, and emphasize that the contribution is the empirical demonstration of performance gains over one-hot labels. revision: yes

  2. Referee: [Results] Results and data description: The 968 jointly annotated radiographs are used only for separate per-task training; no joint model, cross-task loss, or analysis of KL-CPPD co-occurrence is presented, leaving the background claim of asymmetry unaddressed by the experiments.

    Authors: The jointly annotated cases were used exclusively for separate per-task training and evaluation. No joint model, cross-task loss, or co-occurrence analysis was performed, as the study scope was limited to validating soft-labelling for each grading task independently. The background reference to asymmetry draws from clinical literature rather than our results. We will revise the manuscript to remove any implication that the experiments address asymmetry and will add a future-work statement on multi-task or joint modeling. revision: yes

  3. Referee: [Results] Evaluation: Performance improvements are reported on QWK/MAE but no ablation compares the chosen unimodal forms against alternatives (e.g., learned label smoothing or empirical inter-rater distributions), so it is unclear whether gains exceed what standard regularization would achieve.

    Authors: We acknowledge that the current evaluation lacks ablations against other regularization strategies. We will add an ablation study comparing the four soft-labelling distributions against standard label smoothing (multiple epsilon values) using the same backbone and metrics. The revised results section will report these comparisons to clarify whether the unimodal forms provide benefits beyond generic smoothing. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparison of fixed heuristic label encodings on collected data

full rationale

The paper performs an empirical study: 2172 radiographs (968 jointly annotated) are used to train ordinal DL models under one-hot vs. four fixed unimodal soft-label distributions (binomial, beta, triangular, exponential) centered on the annotated grade. Performance is measured by QWK, MAE, AMAE, MMAE with statistical tests. No equations derive a target quantity from fitted parameters within the paper; the distributions are chosen as alternative encodings rather than learned or self-referential. No self-citation chain, uniqueness theorem, or ansatz smuggling supports a central claim. The work is self-contained against external benchmarks (held-out test performance) and does not reduce any reported result to a quantity defined by its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based solely on abstract; no explicit free parameters, invented entities, or additional axioms described beyond standard assumptions of supervised learning on annotated medical images.

axioms (1)
  • domain assumption The 968 jointly annotated radiographs provide accurate ground-truth grades that reflect clinical severity and the observed asymmetry between scales.
    Framework trains and evaluates directly against these annotations as targets.

pith-pipeline@v0.9.1-grok · 5880 in / 1091 out tokens · 48289 ms · 2026-06-29T13:07:03.704290+00:00 · methodology

discussion (0)

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Reference graph

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