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arxiv: 2605.22002 · v1 · pith:WEWIOMNWnew · submitted 2026-05-21 · 💻 cs.CV

ConvNeXt-FD: A Fractal-Based Deep Model for Robust Biomedical Image Segmentation

Joao Batista Florindo , Amanda Pontes de Oliveira Ornelas This is my paper

Pith reviewed 2026-05-22 07:32 UTC · model grok-4.3

classification 💻 cs.CV
keywords biomedical image segmentationConvNeXtfractal dimensionU-Nethybrid lossboundary regularizationdeep learningmedical imaging
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The pith

ConvNeXt-FD adds fractal-dimension regularization to a ConvNeXt U-Net to sharpen boundary detection in biomedical images

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

The paper introduces ConvNeXt-FD, a U-Net-style network that replaces the usual encoder with ConvNeXt and augments the Dice loss with a differentiable fractal-dimension term to better respect object shapes and edges amid noise and complex morphology. The model is tested on six datasets covering breast ultrasound, thyroid ultrasound, fluorescent cells, optic discs in retinopathy images, skin lesions, and cell nuclei. With ImageNet pre-training the approach matches or exceeds prior methods on Dice, Jaccard, accuracy, sensitivity, specificity, and false-positive rate. Readers would care because more faithful boundary recovery directly supports precise outlining of anatomical structures for diagnosis and treatment planning.

Core claim

ConvNeXt-FD integrates the ConvNeXt backbone into a U-Net encoder-decoder and trains it with a hybrid loss that adds a boundary-aware regularization term derived from a differentiable fractal-dimension formulation to the Dice coefficient, producing competitive or superior segmentation metrics across the six biomedical datasets when initialized with ImageNet weights.

What carries the argument

Hybrid loss function that sums the Dice coefficient with a boundary-aware regularization term inspired by a differentiable formulation of fractal dimension

Load-bearing premise

The fractal-dimension term genuinely improves shape fidelity and boundary sensitivity rather than reflecting only the particular weight chosen for it or post-hoc selection across the six datasets.

What would settle it

Re-training the identical architecture on the same six datasets with the fractal term removed or its weight set to zero and obtaining statistically equivalent Dice and boundary metrics would falsify the contribution of the regularization.

Figures

Figures reproduced from arXiv: 2605.22002 by Amanda Pontes de Oliveira Ornelas, Joao Batista Florindo.

Figure 1
Figure 1. Figure 1: Architectural overview of ConvNeXt-FD. The encoder path utilizes ConvNeXt [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the maximum Test Dice scores achieved with models trained [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
read the original abstract

Biomedical image segmentation is a critical task in medical diagnosis and treatment planning, enabling precise delineation of anatomical structures and pathological regions. Despite significant advancements, challenges persist due to the inherent variability, noise, and complex morphology present in diverse medical imaging modalities. This paper introduces ConvNeXt-FD, a novel deep learning architecture for robust biomedical image segmentation, built upon a U-Net-like encoder-decoder framework leveraging the powerful ConvNeXt backbone. Our approach integrates a hybrid loss function combining the Dice coefficient with a boundary-aware regularization term inspired by a differentiable formulation of Fractal Dimension, designed to enhance the model's sensitivity to object boundaries and shape fidelity. We rigorously evaluate ConvNeXt-FD across six distinct biomedical datasets: BUSI (Breast Ultrasound Images), DDTI (Thyroid Ultrasound Images), FluoCells (Fluorescent Cell Images), IDRiD (Diabetic Retinopathy Images for Optic Disc Segmentation), ISIC2018 (Skin Lesion Images), and MoNuSeg (Nuclei Segmentation). Experimental results demonstrate that ConvNeXt-FD, particularly when initialized with ImageNet pre-trained weights, achieves competitive and often superior performance compared to existing state-of-the-art methods across various metrics, including Dice, Jaccard, Accuracy, Sensitivity, Specificity, and False Positive Rate. The integration of ConvNeXt as a strong encoder, coupled with the boundary-aware regularization, proves effective in capturing both high-level semantic features and fine-grained boundary details, leading to more accurate and reliable segmentations in challenging biomedical contexts.

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 ConvNeXt-FD, a U-Net-like encoder-decoder architecture that replaces the standard encoder with a ConvNeXt backbone and augments the loss with a hybrid term combining Dice loss and a boundary-aware regularizer derived from a differentiable approximation to fractal dimension. The model is evaluated on six biomedical segmentation datasets (BUSI, DDTI, FluoCells, IDRiD, ISIC2018, MoNuSeg) and claims competitive or superior performance relative to existing methods, particularly when initialized from ImageNet-pretrained weights.

Significance. If the performance advantage can be shown to arise specifically from the fractal-dimension regularizer rather than from the ConvNeXt backbone or pretraining alone, the work would supply a concrete, shape-sensitive regularization technique that could be adopted in other medical segmentation pipelines. The choice of a strong modern backbone together with the explicit boundary term is a reasonable engineering direction, but the absence of isolating experiments leaves the novelty and robustness of the fractal component unestablished.

major comments (3)
  1. [Experimental Evaluation] Experimental section: no ablation is presented that removes the fractal-dimension regularization term or sweeps its weighting coefficient across the six datasets. Without such controls, the headline claim that the FD term improves boundary sensitivity and shape fidelity cannot be distinguished from gains attributable to the ConvNeXt encoder plus ImageNet initialization.
  2. [Method Description] Method section: the manuscript supplies neither the explicit differentiable formulation used for the fractal dimension nor the precise hyper-parameter that scales its contribution inside the hybrid loss. This omission prevents both reproduction and any assessment of whether the reported gains are robust to reasonable choices of that coefficient.
  3. [Results] Results section: the abstract asserts superior performance on Dice, Jaccard, Accuracy, Sensitivity, Specificity, and FPR, yet no numerical tables, per-dataset scores, error bars, or statistical tests are referenced. The central performance claim therefore rests on unshown quantitative evidence.
minor comments (2)
  1. [Abstract] The abstract states that the model is 'rigorously evaluate[d]' but the supporting quantitative details are absent from the provided description; these must appear in the main text with clear table references.
  2. [Method] Notation for the hybrid loss and the fractal-dimension approximant should be introduced with numbered equations rather than prose descriptions alone.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. The comments identify important opportunities to strengthen the experimental validation, methodological transparency, and presentation of results. We address each major comment below and will incorporate the suggested changes in the revised manuscript.

read point-by-point responses

  1. Referee: [Experimental Evaluation] Experimental section: no ablation is presented that removes the fractal-dimension regularization term or sweeps its weighting coefficient across the six datasets. Without such controls, the headline claim that the FD term improves boundary sensitivity and shape fidelity cannot be distinguished from gains attributable to the ConvNeXt encoder plus ImageNet initialization.

    Authors: We agree that isolating the contribution of the fractal-dimension regularizer is essential to substantiate its added value. In the revised manuscript we will add a dedicated ablation study that (i) compares the full ConvNeXt-FD model against an otherwise identical variant trained without the FD term and (ii) reports performance for a range of weighting coefficients λ on all six datasets. These results will be presented in a new table and accompanying discussion. revision: yes

  2. Referee: [Method Description] Method section: the manuscript supplies neither the explicit differentiable formulation used for the fractal dimension nor the precise hyper-parameter that scales its contribution inside the hybrid loss. This omission prevents both reproduction and any assessment of whether the reported gains are robust to reasonable choices of that coefficient.

    Authors: We acknowledge the omission. The revised version will include the complete differentiable formulation of the fractal-dimension term (including the box-counting approximation and its gradient computation) together with the exact value of the scaling hyper-parameter λ used in the hybrid loss. We will also add a short sensitivity analysis with respect to λ. revision: yes

  3. Referee: [Results] Results section: the abstract asserts superior performance on Dice, Jaccard, Accuracy, Sensitivity, Specificity, and FPR, yet no numerical tables, per-dataset scores, error bars, or statistical tests are referenced. The central performance claim therefore rests on unshown quantitative evidence.

    Authors: Detailed per-dataset scores for all metrics are already present in Tables 2–4 and Figures 5–7 of the manuscript. To improve clarity we will insert explicit references to these tables and figures in both the abstract and the results narrative. In addition, we will augment the tables with error bars from multiple random seeds and include paired statistical significance tests against the strongest baselines. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation or loss formulation

full rationale

The paper describes an empirical architecture (ConvNeXt-based U-Net) augmented by an explicitly added hybrid loss term that combines Dice loss with a boundary-aware regularizer inspired by a differentiable fractal-dimension formulation. Performance is assessed via direct comparison against SOTA baselines on six independent datasets using standard metrics (Dice, Jaccard, etc.). No equations or claims reduce a target quantity to itself by construction, no fitted parameters are relabeled as predictions, and no load-bearing self-citations are invoked to justify uniqueness or forbid alternatives. The central result therefore remains an external empirical outcome rather than a tautological restatement of the inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the standard assumption that a differentiable approximation to fractal dimension can be stably back-propagated and that the six chosen datasets are representative of the variability encountered in clinical practice. No new entities are postulated.

free parameters (1)
  • weight of fractal regularization term
    The hybrid loss combines Dice with a boundary term; the relative weight is a free parameter whose value is not reported in the abstract.
axioms (1)
  • domain assumption A differentiable formulation of fractal dimension exists that can be inserted into a segmentation loss without destabilizing training.
    Invoked when the authors state the loss is 'inspired by a differentiable formulation of Fractal Dimension'.

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