Modelling Geographic Atrophy Progression using Implicit Neural Representations

Christina Bornberg; Florentin Bieder; Paul Friedrich; Peter Maloca; Philippe Cattin; Philippe Valmaggia; Simone Sarrocco

REVIEW 4 major objections 5 minor 26 references

Modelling Geographic Atrophy Progression using Implicit Neural Representations

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read An implicit neural representation with a per-eye latent vector models geographic atrophy as a continuous trajectory and predicts future FAF images and GA segmentations, reaching DICE 0.91 in test-time adaptation.

desk verdict A plausible first INR-based model for geographic atrophy progression, with a sensible joint reconstruction/segmentation design, but the headline comparison rests on 6 test eyes and a duplicated baseline row in Table 1, so the evidence is thinner than the abstract suggests. read the letter →

arxiv 2608.10807 v1 pith:QZTSZ7NQ submitted 2026-08-11 cs.CV cs.AI

Simone Sarrocco , Paul Friedrich , Florentin Bieder , Christina Bornberg , Philippe Valmaggia , Peter Maloca , Philippe Cattin This is my paper · ORCID

classification cs.CVcs.AI

keywords implicitneuralrepresentationsgeographicatrophyage-relatedmaculardegenerationdiseaseprogressionfundusautofluorescencetest-timeadaptationimagesegmentationlongitudinalmodelling

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

The paper sets out to establish that a single implicit neural representation, conditioned on an eye-specific latent vector plus time and age, can capture the full geographic-atrophy trajectory of an individual eye from a handful of fundus autofluorescence images. If this is right, the same model can generate previously unseen FAF images and GA segmentations at past, intermediate, and future time points, which matters because GA progression is highly individualised and hard to forecast. In the main test-time adaptation scenario the model reports DICE 0.91 and lesion-area MAE 0.20 mm² for future segmentations, and the lowest lesion-area MAE (0.15 mm²) for interpolating a held-out visit among the methods compared. A sympathetic reader would take the paper's claim to be that disease progression in GA is smooth enough in latent space to be learned and extrapolated per patient, even when training data are scarce.

What carries the argument

The central object is a time-conditioned implicit neural representation (INR): an auto-decoding multi-layer perceptron with SIREN periodic activations that carries a shared set of weights $\theta$ for all eyes. Each eye $i$ owns a spatial latent vector $z_i \in \mathbb{R}^{C\times X_1\times X_2}$, sampled at a coordinate $x$ by bilinear interpolation and concatenated with the time $t$ (weeks since baseline) and the patient's age $\mathrm{age}_t$; modulation layers map this combined code into per-layer scale and shift, so the same network is steered into each individual's trajectory. The network splits into a reconstruction head $f^{\mathrm{faf}}_\theta$ that outputs FAF pixel intensity (MSE loss) and a segmentation head $f^{\mathrm{seg}}_\theta$ that consumes the last two hidden layers and outputs a two-class GA probability (DICE plus binary cross-entropy loss). Training optimises the joint loss over all eyes and visits, and test-time adaptation freezes $\theta$ while optimising only the new eye's latent against the available visits, so a single forward pass generates the requested past, intermediate, or future image and segmentation. This trajectory-in-latent-space mechanism is what carries the paper's claim.

What would settle it

Take an eye with at least three visits in which the GA lesion grows a new disconnected atrophic island between visits instead of only expanding the existing boundary. Fit the model on the first two visits, hold out the third, and check whether the predicted segmentation contains the island. Because the per-eye latent is shared and the trajectory is continuous, the model can only deform the existing lesion; missing the new island at the held-out visit would falsify the smooth single-trajectory assumption.

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Extended reading notes

Core claim

The paper claims that geographic atrophy (GA) progression in late dry age-related macular degeneration can be modelled as a continuous, patient-specific trajectory rather than as a sequence of independent visit images. Concretely, a shared implicit neural representation, fitted jointly over many eyes, is conditioned by each eye's own latent vector together with the time elapsed since baseline and the patient's age, and is trained to output both the FAF image intensity and the GA segmentation label at any queried coordinate. At test time the shared network is frozen and only the new eye's latent is optimised on the available visits; a single forward pass then yields held-out past, missing, and future images and segmentations. On an in-house longitudinal cohort of 37 eyes the method reports the best segmentation metrics among compared methods in the test-time adaptation scenario (DICE 0.91, Hausdorff distance 6.78 px, lesion-area MAE 0.20 mm²) and the lowest lesion-area MAE for interpolating a missing visit (0.15 mm²), at image reconstruction quality comparable to the baselines. The paper's conclusion is that INR-based trajectory modelling is a viable low-data way to forecast individual lesion shape and area.

Load-bearing premise

The load-bearing premise is that each eye's geographic atrophy follows one smooth, continuous trajectory that a single low-dimensional latent vector, combined with time and age, can represent; if a lesion grows in jumps, appears in new disconnected places, or the latent cannot separate stable anatomy from visit-specific noise, the predicted segmentations will be inaccurate even when the model fits its training data.

Editorial extensions

If this is right

A clinician could fit a new patient's eye from one or two visits and generate the expected GA lesion shape and area at any future or intermediate time, helping to communicate prognosis.
Because the model produces both FAF images and segmentations at arbitrary query times, lesion-area MAE can be read off at the exact time point a trial protocol specifies, without waiting for that visit to occur.
The method works with only 26 training eyes, so INR-based trajectory modelling is a viable route in rare or low-data medical-imaging settings where large annotated longitudinal cohorts do not exist.
The reported best-case numbers (DICE 0.91, MAE 0.20 mm² in Scenario 2; DICE 0.87, MAE 0.15 mm² for missing visits) support using the model to monitor disease evolution at the individual level.

Reading between the lines

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

Beyond the paper, the same latent-trajectory machinery could transfer to other slowly progressing, sparsely sampled diseases such as glaucoma or diabetic retinopathy, provided the smoothness assumption is verified; nothing in the paper tests that transfer.
Beyond the paper, the latent vector space could be probed by interpolating between two eyes' latents to generate intermediate anatomies, a check the paper does not perform but which would directly test whether the representation is a true progression manifold.
Beyond the paper, a comparison on longer follow-up with more visits would likely widen the gap over copy-forward, since the paper itself notes that the short follow-up period makes copy-forward surprisingly strong on image reconstruction metrics.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

What to know: this is the first application of implicit neural representations to modelling geographic atrophy progression, and it does something sensible with them. It couples a FAF reconstruction head and a GA segmentation head on a shared modulated INR, with per-eye latent vectors and time/age conditioning. The two-layer feature concatenation into the segmentation head is a small but real tweak over prior work. The writing is clear, the method is reproducible (code is released), and the authors are refreshingly honest in the conclusion that copy-forward gives the best FAF reconstruction in their short follow-up setting.

The soft spots are real but addressable. The abstract claims the method delivers the lowest lesion-area MAE and highest DICE "without sacrificing FAF image quality," yet Table 1 shows copy-forward outperforming the method on PSNR, SSIM, and LPIPS in both Scenario 1 and Scenario 2. The conclusion already admits this, so the abstract just needs to be aligned with the evidence. Bigger issue: Table 1 Scenario 2 lists Linear extrap. with exactly the same metrics as Copy-forward (17.86 / 0.61 / 0.14 / 0.86 / 6.98 / 0.38). That is a copy-paste error, and it undermines confidence in the numerical comparison until fixed. Finally, the test set is six eyes. The headline numbers—DICE 0.91 vs 0.86, MAE 0.20 vs 0.38—come with overlapping error bars and no significance test. On six eyes, a paired test would likely leave the superiority claim unproven. That is the biggest scientific weakness, and it is a matter of reporting rather than a flawed method.

The method itself is a reasonable extension of prior INR progression work to a new medical domain, and the missing-visit interpolation results are the most convincing part of the evaluation. The paper is for ophthalmic image analysis researchers and INR practitioners looking for clinical applications. It deserves a serious referee: the idea is worth publishing, but the claims need to be scaled back, the table fixed, and ideally some uncertainty quantification or a larger test set added. I would not desk-reject it.

Referee Report

4 major / 5 minor

Summary. The paper proposes a time-conditioned implicit neural representation (INR) with per-eye latent codes to jointly model Fundus Autofluorescence (FAF) image appearance and Geographic Atrophy (GA) segmentation over time. The method uses an auto-decoder MLP with SIREN activations, FiLM modulation conditioned on the latent vector, time in weeks, and patient age, and is split into a reconstruction head and a segmentation head. Test-time adaptation optimizes a new latent code on a subset of visits of an unseen eye while keeping the INR frozen, then predicts held-out past, future, or intermediate visits. The method is evaluated on the OMEGA longitudinal FAF dataset in three scenarios: single-pair extrapolation, test-time adaptation with full patient history, and missing-visit interpolation. The authors report competitive or best segmentation quality (DICE, Hausdorff distance, lesion-area MAE) and competitive FAF reconstruction, with code released publicly.

Significance. If the results hold, this is a useful extension of implicit neural representations to longitudinal ophthalmic imaging, enabling continuous, patient-specific disease trajectories from very limited data and providing both image-level and segmentation-level predictions. The paper has several strengths: it uses a patient-wise data split, evaluates on held-out visits without leaking the target visit into the latent optimization, provides an ablation of latent-grid configurations, and releases code. However, the evidence supporting the headline superiority claim is weakened by the very small test set (n=6), the absence of significance testing, and a clear numerical inconsistency in Table 1. The abstract overstates FAF image-quality performance relative to the paper's own quantitative results and conclusion. These issues are addressable, and the underlying modeling idea is plausible, so the contribution is worth considering after substantial revision.

major comments (4)

[Abstract and Table 1] The abstract states the method achieves the lowest MAE and highest DICE 'without sacrificing FAF image quality,' but Table 1 contradicts this: in Scenario 1, Ours has lower PSNR than Copy-forward (16.19 vs 16.49) and higher LPIPS (0.28 vs 0.16); in Scenario 2, Copy-forward achieves higher PSNR (17.86 vs 16.31), higher SSIM (0.61 vs 0.61, tied), and lower LPIPS (0.14 vs 0.26). The conclusion also explicitly acknowledges that copying the last image yields the best reconstruction quality. The abstract should be revised to report the segmentation advantages only, or to qualify the FAF claim consistently with the presented numbers.
[Table 1, Scenario 2] The row for 'Linear extrap. [12]' reports exactly the same values as 'Copy-forward' (PSNR 17.86, SSIM 0.61, LPIPS 0.14, DICE 0.86, HD 6.98, MAE 0.38). This is implausible as a real result and appears to be a copy-paste error. Because these rows are used to support the claim that the method outperforms classical baselines, the numerical integrity of the comparison must be verified and corrected before the results can be assessed.
[Section 4 and Table 1 (statistical evaluation)] The central claim that the method is better than the baselines rests on only six test eyes, and no significance tests or confidence intervals are provided. For Scenario 2, the reported DICE is 0.91±0.05 versus 0.86±0.09 for Copy-forward, and the lesion-area MAE is 0.20±0.29 versus 0.38±0.24; these standard deviations overlap considerably at n=6. The authors should report paired tests (e.g., Wilcoxon signed-rank or paired t-test) with effect sizes, or otherwise provide per-eye differences, for DICE, MAE, and HD in all scenarios. Without this, the assertion of superior progression prediction is not statistically established.
[Table 1, Scenario 2 and Missing visits] T-I2SBUNet [16] is listed as a comparison method and appears in Scenario 1, but it is absent from Scenario 2 and from the Missing-visits table. If the comparison is intended to cover all scenarios, the omission should be explained, or the method should be included. This is relevant because the qualitative comparison in Fig. 2 may not represent all methods in all settings.

minor comments (5)

[Section 3, Implementation Details] The sentence 'The hyperparameters were optimised on the validation set' would benefit from a full list of searched hyperparameter ranges and the selection criterion; otherwise the reproducibility of the configuration choice is limited.
[Figure 5 caption] The caption states the red box is the best configuration 'by subjective judgment over all five metrics.' Please define the selection rule explicitly so that the choice of C=256 and H=W=32 is reproducible rather than subjective.
[Section 4, Hyperparameter Selection] The text says 'we noticed that encoding time as an input coordinate, similar to [3], consistently underperformed FiLM modulation,' but no quantitative comparison is shown for this design decision. A small table or mention in the ablation figure would strengthen this claim.
[Section 3, Comparison Methods] In the Missing-visits scenario, only classical interpolation methods are compared; the absence of DL baselines in this scenario should be stated explicitly in the text, since it currently reads as a broader comparison.
[Table 1 header] The header 'Extrapola tion' contains an unnecessary space; this is a trivial typo but should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: held-out test-eye predictions are genuine extrapolations compared against external baselines.

full rationale

The derivation chain is self-contained. The INR is trained on the training eyes' FAF images and GA segmentation masks; for a held-out eye a fresh latent vector is optimized only on the N-1 observed visits while the network weights stay frozen, and the held-out visit is produced by a forward pass f_theta(x | z_k) through the unchanged network. No predicted quantity is defined as, or fitted to, the target value: each scenario (Scenario 1, Scenario 2, missing-visit interpolation) excludes the evaluated visit from the latent optimization. The comparisons are against external baselines (ImageFlowNet, T-UNet, T-I2SBUNet, classical interpolation and copy-forward) on the same held-out visits, so the central empirical claim is not forced by the method's construction. The paper's self-citations to Bieder et al. [3], Dannecker et al. [4,5], and Friedrich et al. [9] supply only architectural ingredients (per-subject latent codes, 3D latent grids, SIREN/FiLM conditioning, segmentation heads) and are not load-bearing for the headline result; no uniqueness theorem or ansatz is imported from the authors' own prior work to forbid alternatives. The conclusion candidly states that copy-forward achieves the best FAF reconstruction in some scenarios and that extrapolation image quality remains a challenge; this undercuts the abstract's 'without sacrificing FAF image quality' phrasing, but it is a consistency and evidence-weighting issue, not a circular reduction. The small test set (n=6 eyes), overlapping error bars, absence of significance tests, and the duplicated Linear extrap./Copy-forward row in Table 1 are statistical and reporting concerns that belong under correctness risk, not circularity.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The paper does not introduce new physical or conceptual entities. The per-eye latent vector and spatial latent grid are standard INR components inherited from prior work (Dannecker et al., CINeMA, NISF), not new claims about nature.

free parameters (6)

Latent vector spatial grid size = 32x32
Hyperparameter selected by validation grid search (Fig. 5); controls the trade-off between FAF reconstruction and segmentation quality.
Latent vector channels C = 256
Selected by validation grid search; higher channels improve image quality but hurt segmentation.
Reconstruction loss weight alpha = 10
Set to 10 following [23] as in the NISF segmentation paper; not tuned on this dataset.
SIREN frequency omega0 = 30
Set following SIREN [22].
Optimizer learning rates (INR, latent) = 1e-4, 5e-3
Chosen by validation; AdamW with weight decay 0.1.
Test-time optimization epochs = 25
Number of latent-vector optimization steps for a new eye; set by validation.

assumptions (4)

domain assumption GA progression follows a continuous, patient-specific trajectory over time.
Section 1 states: 'Our modelling assumption is that the GA progression follows a continuous, patient-specific trajectory.' The model represents time as a continuous input.
domain assumption One latent vector per eye, shared across all visits, is sufficient to capture that eye's disease state.
Section 2: 'we assign one latent vector to each individual eye shared across all its images.' This forces visit-invariant identity representation.
domain assumption Spatial coordinates and conditioning variables are normalized and the FAF images are pre-registered across visits.
Section 3: 'The FAF images were pre-registered intra-patient by aligning each follow-up visit to its baseline.' Without registration, pixel-wise latent conditioning is ill-defined.
domain assumption Semiautomatic annotations from three graders aggregated by majority voting provide reliable ground-truth segmentation.
Section 3 describes the annotation protocol; segmentation loss is trained against this human-derived ground truth.

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Cite this review

Pith. "Pith review of Modelling Geographic Atrophy Progression using Implicit Neural Representations." pith.science (2026). https://pith.science/paper/QZTSZ7NQ

@misc{pith2026260810807,
  author       = {Pith},
  title        = {Pith review of: Modelling Geographic Atrophy Progression using Implicit Neural Representations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QZTSZ7NQ}},
  note         = {Machine review of arXiv:2608.10807}
}

read the original abstract

Age-related Macular Degeneration (AMD) is the major cause of blindness in the Western world. Its late dry phase is characterised by irreversible atrophic areas, namely Geographic Atrophy (GA). Longitudinal Fundus Autofluorescence (FAF) image acquisitions are currently the main tool for assessing lesion growth over time at the image level. However, due to its highly individualised progression, the evolution of late AMD remains poorly understood. In this work, we propose using Implicit Neural Representations (INRs) to model GA progression at the individual level in a low-data setting. Our approach generates both FAF and GA segmentation at both past and future time points. Among the comparison models, our method achieves competitive segmentation quality across different scenarios, yielding the lowest Mean Absolute Error (MAE) for the GA lesion area and the highest DICE score, without sacrificing FAF image quality. The code is available at https://github.com/SimoneSarrocco/ga-progression-with-inrs.

Figures

Figures reproduced from arXiv: 2608.10807 by the authors.

**Figure 1.** Our proposed model architecture. In the training phase (a), a spatial coordinate x ∈ R 2 is fed into the MLP. Each layer of the MLP is conditioned by concatenating the latent vector zi, the time in weeks from the baseline visit, t, and the age of the patient at t, aget , via modulation. The shared INR is split into reconstruction head f faf θ , which outputs the pixel intensity value Iˆi(x) (purple cross in the outp… view at source ↗

**Figure 2.** Qualitative comparison between all different methods. In the first row, we show an example of Scenario 1 ; in the second row, an example of Scenario 2 for the same test eye. PSNR, DICE score, and MAE are reported for each prediction [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Individual longitudinal prediction of a subject of the test set. First and third row: the four ground truth (GT) FAF and GA segmentation masks are shown. Second row: reconstructed existing visits (yellow), predicted interpolated (light blue) and extrapolated (purple) FAF images are provided. The last row displays the change maps for each predicted segmentation at time t with respect to the last available GT [PITH_… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Longitudinal analysis of the individual lesion area trajectories. The six subjectspecific predicted trajectories are compared with linear extrapolation, cubic B-spline extrapolation, and copy-forward. Linear and cubic B-spline extrapolation curves are fitted using all…

**Figure 5.** Figure 5: Latent-grid ablation over number of channels C (rows) and spatial resolution H = W (columns). Each cell reports a metric at the checkpoint with the best DICE + lesion-area-MAE trade-off (lighter is better ). The red box is the best configuration (C=256, H = W = 32) b…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [12]

IEEE Transactions on Acous- tics, Speech, and Signal Processing31(3), 746–749 (Jun 1983)

Kay, S.: Some results in linear interpolation theory. IEEE Transactions on Acous- tics, Speech, and Signal Processing31(3), 746–749 (Jun 1983)

work page 1983

[2] [16]

Liu, G.H., et al.: I$^2$SB: Image-to-Image Schrödinger Bridge (May 2023)

work page 2023

[3] [1]

Ophthalmic Research66(1), 1392–1401

Ansari, G., Schärer, N., Camenzind Zuche, H., Gabrani, C., Anders, P., Pfau, K., Valmaggia, P., Giani, A., Esmaeelpour, M., Chingning Yamaguchi, T., Prünte, C.F., Maloca, P.M., Schmetterer, L., Scholl, H.P.N., Pfau, M.: The Optical Coher- ence Tomography and Microperimetry Biomarker Evaluation in Patients with Geo- graphic Atrophy (OMEGA) Study: Design an...

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