Probabilistic Modeling of Multi-rater Medical Image Segmentation for Diversity and Personalization

Chunhua Shen; Ke Liu; Shangde Gao; Shangqi Gao; Shuaike Shen; Yichao Fu

arxiv: 2512.00748 · v2 · submitted 2025-11-30 · 💻 cs.CV · cs.AI

Probabilistic Modeling of Multi-rater Medical Image Segmentation for Diversity and Personalization

Ke Liu , Shangde Gao , Yichao Fu , Shuaike Shen , Shangqi Gao , Chunhua Shen This is my paper

Pith reviewed 2026-05-17 03:32 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords multi-rater medical image segmentationprobabilistic modelinglatent variablesvariational inferencelesion boundary ambiguityexpert personalizationdiverse segmentationnasopharyngeal carcinoma

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The pith

ProSeg uses two latent variables and variational inference to produce both diverse and expert-personalized segmentations for medical images.

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

The paper aims to solve the problem where previous multi-rater segmentation models could either create varied outputs without matching specific experts or copy individual annotators without diversity. It proposes ProSeg, which models expert preferences and boundary ambiguity as separate latent variables. By using variational inference to learn their distributions, the model generates segmentations by sampling from them. This matters because medical images often have unclear boundaries and experts disagree, so better handling of this uncertainty could improve AI tools for diagnosis. Experiments on nasopharyngeal carcinoma and lung nodule datasets show it reaches new state-of-the-art results.

Core claim

We propose Probabilistic modeling of multi-rater lesion Segmentation (ProSeg) that simultaneously enables both diversification and personalization. Specifically, we introduce two latent variables to model expert annotation preferences and lesion boundary ambiguity. Their conditional probabilistic distributions are then obtained through variational inference, allowing segmentation outputs to be generated by sampling from these distributions. Extensive experiments on both the nasopharyngeal carcinoma dataset (NPC) and the lung nodule dataset (LIDC-IDRI) demonstrate that our ProSeg achieves a new state-of-the-art performance, providing segmentation results that are both diverse and expert-pres

What carries the argument

Two latent variables, one for expert annotation preferences and one for lesion boundary ambiguity, whose distributions are learned via variational inference to enable sampling of diverse and personalized segmentations.

Load-bearing premise

Introducing two separate latent variables for expert preferences and boundary ambiguity will allow simultaneous diversification and personalization without any loss in segmentation accuracy.

What would settle it

A test where increasing the diversity of outputs causes the personalized matches to specific experts to degrade significantly, or vice versa, on the LIDC-IDRI dataset would falsify the claim.

Figures

Figures reproduced from arXiv: 2512.00748 by Chunhua Shen, Ke Liu, Shangde Gao, Shangqi Gao, Shuaike Shen, Yichao Fu.

**Figure 1.** Figure 1: Distance distribution between two random experts. A greater distance indicates higher diversity and a more similar distribution with the Gold standard indicates better personalization. Medical image segmentation is of great importance for automatic diagnosis and treatment planning in clinical practice Isensee et al. (2021). However, the task is challenging due to the inherent uncertainty of data, such a… view at source ↗

**Figure 2.** Figure 2: Probability graph model (PGM) of methods for multi-rater segmentation. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Model architecture of deep variational inference for multi-rater segmentation. ProSeg [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Expert annotator rank distribution of test (second row) and train (first row) datasets, where [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

**Figure 5.** Figure 5: Example of Dmax and Dmatch calculation in a given 4 × 5 Dice matrix. Random distance to two experts We define the distance between experts as the IoU distance as follows: dIoU (S1, S2) = 1 − |S1 ∩ S2| |S1 ∪ S2| (22) where |S1 ∩ S2| is the area of the intersection of S1 and S2, and |S1 ∪ S2| is the area of the union of S1 and S2. In [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: Class embedding distribution Dirichlet distribution of Expert. We randomly sample 300 samples from the posterior distribution of p(τ |r) for each expert. Then we use tsne (Van der Maaten & Hinton, 2008) to project the 8- 17 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗

**Figure 7.** Figure 7: Performance on multi-rater medical image segmentation [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗

**Figure 8.** Figure 8: Distribution of pair distance between two experts. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗

**Figure 9.** Figure 9: Visual results of segmentation on NPC dataset. Each row from the top to bottom indicates [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗

**Figure 10.** Figure 10: Visual results of segmentation on NPC dataset. Each row from the top to bottom indicates [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗

**Figure 11.** Figure 11: Visual results of segmentation on LIDC-IDRI dataset. Each row from the top to bottom [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗

**Figure 12.** Figure 12: Visual results of segmentation on LIDC-IDRI dataset. Each row from the top to bottom [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗

read the original abstract

Lesion segmentation is inherently influenced by imaging uncertainty, arising from ill-defined lesion boundaries and inter-observer variability in diagnosis. To address this challenge, previous works formulated the multi-rater medical image segmentation task, where multiple experts provide separate annotations for each image. However, existing models are typically constrained to either generate diverse segmentation that lacks expert specificity or to produce personalized outputs that merely replicate individual annotators. We propose \textbf{Pro}babilistic modeling of multi-rater lesion \textbf{Seg}mentation (\textbf{ProSeg}) that simultaneously enables both diversification and personalization. Specifically, we introduce two latent variables to model expert annotation preferences and lesion boundary ambiguity. Their conditional probabilistic distributions are then obtained through variational inference, allowing segmentation outputs to be generated by sampling from these distributions. Extensive experiments on both the nasopharyngeal carcinoma dataset (NPC) and the lung nodule dataset (LIDC-IDRI) demonstrate that our ProSeg achieves a new state-of-the-art performance, providing segmentation results that are both diverse and expert-personalized.

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.

Desk Editor's Note private letter to a colleague

ProSeg adds two separate latents for expert preference and boundary ambiguity to handle both diversity and personalization at once in multi-rater lesion segmentation, but the SOTA claim is hard to assess without the actual numbers and checks on latent independence.

read the letter

This paper's main contribution is a model called ProSeg that introduces two separate latent variables in a variational setup—one for modeling expert-specific annotation preferences and another for lesion boundary ambiguity—to produce segmentations that are both diverse across raters and personalized to individual experts. It does a good job framing the problem around real clinical needs in medical imaging, where inter-rater variability and boundary uncertainty are common issues in lesion segmentation. The choice of NPC and LIDC-IDRI datasets is appropriate for testing this, as they involve multiple annotations per image. What is new here is the explicit separation of these two factors into distinct latents, allowing independent control: you can personalize to an expert while varying the ambiguity for diversity, or vice versa. This seems like a targeted extension beyond models that only do one or the other. The use of variational inference to learn the conditional distributions is standard but applied reasonably to this dual goal. If the full experiments back it up, this could be useful for building more reliable AI tools that account for human variability. On the soft spots, the abstract claims state-of-the-art performance but doesn't show any specific metrics, baselines, or ablation results. Without those, it's difficult to judge how much better it really is or if the improvements come from the dual latent design. The stress-test concern about whether the latents remain disentangled under the approximate posterior is valid to check; if they correlate, sampling one while conditioning on the other could introduce unintended shifts in the output distribution. The paper appears to engage honestly with the literature on probabilistic segmentation, without obvious circularity. This work is aimed at the medical imaging and computer vision community, particularly those working on uncertainty modeling and multi-annotator tasks. A reader focused on practical applications in radiology or oncology AI would get the most value, as it directly addresses consistency in diagnosis support tools. It deserves a serious referee because the idea is grounded in a practical problem and uses established techniques in a new combination. Even if revisions are needed for clearer experiments, the core framing is worth reviewing. I would recommend sending this to peer review rather than desk rejecting it.

Referee Report

1 major / 2 minor

Summary. The paper introduces ProSeg, a variational model for multi-rater medical image segmentation that employs two separate latent variables to capture expert annotation preferences and lesion boundary ambiguity. By sampling from the learned conditional distributions obtained via variational inference, the model aims to produce segmentation maps that are simultaneously diverse (via boundary ambiguity) and personalized to individual experts (via preference latent), claiming new state-of-the-art results on the NPC and LIDC-IDRI datasets.

Significance. If the core modeling assumptions hold, the work would meaningfully advance multi-rater segmentation by addressing the common tension between diversity and personalization. Explicitly separating the two sources of uncertainty via distinct latents, rather than a single entangled representation, offers a principled route to controllable outputs that could benefit clinical workflows requiring both uncertainty quantification and expert-specific references.

major comments (1)

[Section 3] Section 3 (Method), variational inference formulation: the central claim that the two latents can be varied independently—fixing the expert-preference latent while sampling the boundary-ambiguity latent (and vice versa) to achieve both personalization and diversity without accuracy loss—is load-bearing but unsupported by direct evidence. The joint approximate posterior q(z_pref, z_amb | x) can learn correlations; without reported diagnostics such as conditional diversity metrics, latent ablation studies, or accuracy under controlled marginalization on NPC and LIDC-IDRI, it is unclear whether the claimed simultaneous achievement is realized or whether trade-offs are masked by overall metrics.

minor comments (2)

[Abstract] Abstract: the SOTA claim is stated without any numerical metrics, baseline names, or dataset-specific scores; adding a single sentence with key quantitative results would strengthen the summary.
Notation: the definitions of the two latent variables and their conditional distributions are introduced without an explicit diagram or equation block showing the generative model p(y | x, z_pref, z_amb); a compact plate diagram or joint factorization would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of our work and for the constructive major comment. We provide a point-by-point response below.

read point-by-point responses

Referee: [Section 3] Section 3 (Method), variational inference formulation: the central claim that the two latents can be varied independently—fixing the expert-preference latent while sampling the boundary-ambiguity latent (and vice versa) to achieve both personalization and diversity without accuracy loss—is load-bearing but unsupported by direct evidence. The joint approximate posterior q(z_pref, z_amb | x) can learn correlations; without reported diagnostics such as conditional diversity metrics, latent ablation studies, or accuracy under controlled marginalization on NPC and LIDC-IDRI, it is unclear whether the claimed simultaneous achievement is realized or whether trade-offs are masked by overall metrics.

Authors: We acknowledge the validity of this concern. The design of ProSeg introduces two separate latent variables specifically to disentangle expert preferences from boundary ambiguity, with the variational inference providing conditional distributions for sampling. Our reported results demonstrate that the model achieves both diversity (through varying boundary ambiguity) and personalization (through expert preferences) while attaining state-of-the-art performance on the NPC and LIDC-IDRI datasets. However, to directly address potential correlations in the joint posterior and to provide explicit evidence of independent control, we will include in the revised manuscript: (1) latent ablation studies removing one latent at a time, (2) conditional diversity metrics when fixing one latent and varying the other, and (3) segmentation accuracy under controlled marginalization. These additions will confirm that the separation enables simultaneous achievement without hidden trade-offs. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard variational inference on independent latents

full rationale

The derivation introduces two latent variables (expert preference and boundary ambiguity) whose conditional distributions are obtained via variational inference, then samples from them to produce outputs. This follows the standard VAE-style construction for uncertainty modeling and does not reduce any target quantity (diversity or personalization) to a fitted parameter or self-citation by definition. No equations or claims in the provided text equate a prediction to its own input; the SOTA claim rests on external dataset experiments rather than internal redefinition. The approach is self-contained against the usual probabilistic modeling benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 2 invented entities

The model introduces two new latent variables without independent evidence beyond the claim that they enable the desired properties; relies on standard assumptions of variational inference.

invented entities (2)

latent variable for expert annotation preferences no independent evidence
purpose: to model individual rater styles for personalization
Introduced to capture personalization aspect
latent variable for lesion boundary ambiguity no independent evidence
purpose: to model uncertainty for generating diverse outputs
Introduced to enable diversification

pith-pipeline@v0.9.0 · 5490 in / 1230 out tokens · 29415 ms · 2026-05-17T03:32:17.513835+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

we introduce two latent variables τ and Z to model the inter-observer variability in diagnosis and the ambiguity in medical scans, respectively... conditional probabilistic distributions... through variational inference
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

maximizing the evidence lower bound (ELBO)... KL(q(Z|x)||p(Z)) + KL(q(τ|R)||p(τ))

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

[1]

The chain rule of probability: from the chain rule, we can write the joint conditional probability of Y given τ and Z as Eq. 12. Since each yri is conditionally independent given zi andτ i, we can factorize the joint distribution as Eq. 13. p(Y|τ, Z) =p(y r1 ,y r2 , . . . ,yrN |τ, Z)(12) 12 Preprint p(Y|τ, Z) = NY i=1 p(yri |Z, τ)(13)

work page
[2]

Local Markov Assumption: To further simplify the factorization, we assume that each yi only depends on its local variables zi and τi as Eq. 14. This is a common assumption in mixture models, where each data point is generated from a single component of the mixture. Thus, applying this to the previous equation, we get Eq. 15. p(yi|Z, τ) =p(y i|zi, τi)(14) ...

work page arXiv 2023
[3]

When the distance between the annotations of two experts is closer, their performance is more similar on one test set

The distance between expert annotations is consistent with the learned U-Net (each column). When the distance between the annotations of two experts is closer, their performance is more similar on one test set. For the test set of expert A3, A4 is more different with A3 than A2 (0.6663(A4)V .S.0.6449( A2)). Therefore, the U-Net trained on A2 performs bett...

work page
[4]

As shown in Table

Training a U-Net to segment small target is harder than big targets. As shown in Table. 4, the segmentation area of A4 is smaller than the others, thus it performs much worse than the others. 16 Preprint Table 9: DecomposedGED, includingd pp,d pa, andd aa. MethodGED↓d pp ↑d pa ↓d aa(Constant) Prob. U-Net 0.3614 0.0075 0.3320 0.2951 D-Persona (I)0.2133 0.2...

work page arXiv 2008

[1] [1]

The chain rule of probability: from the chain rule, we can write the joint conditional probability of Y given τ and Z as Eq. 12. Since each yri is conditionally independent given zi andτ i, we can factorize the joint distribution as Eq. 13. p(Y|τ, Z) =p(y r1 ,y r2 , . . . ,yrN |τ, Z)(12) 12 Preprint p(Y|τ, Z) = NY i=1 p(yri |Z, τ)(13)

work page

[2] [2]

Local Markov Assumption: To further simplify the factorization, we assume that each yi only depends on its local variables zi and τi as Eq. 14. This is a common assumption in mixture models, where each data point is generated from a single component of the mixture. Thus, applying this to the previous equation, we get Eq. 15. p(yi|Z, τ) =p(y i|zi, τi)(14) ...

work page arXiv 2023

[3] [3]

When the distance between the annotations of two experts is closer, their performance is more similar on one test set

The distance between expert annotations is consistent with the learned U-Net (each column). When the distance between the annotations of two experts is closer, their performance is more similar on one test set. For the test set of expert A3, A4 is more different with A3 than A2 (0.6663(A4)V .S.0.6449( A2)). Therefore, the U-Net trained on A2 performs bett...

work page

[4] [4]

As shown in Table

Training a U-Net to segment small target is harder than big targets. As shown in Table. 4, the segmentation area of A4 is smaller than the others, thus it performs much worse than the others. 16 Preprint Table 9: DecomposedGED, includingd pp,d pa, andd aa. MethodGED↓d pp ↑d pa ↓d aa(Constant) Prob. U-Net 0.3614 0.0075 0.3320 0.2951 D-Persona (I)0.2133 0.2...

work page arXiv 2008