Conformal Prediction Sets for Instance Segmentation

Dan M. Kluger; Kerri Lu; Sherrie Wang; Stephen Bates

REVIEW 2 major objections 6 minor 1 cited by

Conformal Prediction Sets for Instance Segmentation

T0 review · 2 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For a pixel query, the algorithm returns a set of masks and guarantees with probability at least 1−α that one achieves IoU above a user-set threshold with the true object.

desk verdict A genuinely new conformal set-cover method with sound theory, but the experiments select targets on the same calibration data — a fixable flaw that still warrants peer review. read the letter →

arxiv 2602.10045 v2 pith:QG6KGB2D submitted 2026-02-10 cs.CV cs.LGstat.MEstat.ML

Kerri Lu , Dan M. Kluger , Stephen Bates , Sherrie Wang This is my paper · ORCID

classification cs.CVcs.LGstat.MEstat.ML

keywords conformalpredictioninstancesegmentationuncertaintyquantificationIntersection-over-Unionsetssetcovercalibrationpixelqueries

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

This paper aims to give instance segmentation the kind of calibrated uncertainty that conformal prediction provides for classifiers. The authors propose an algorithm that, given an image and a pixel coordinate query, returns a small set of candidate object masks, chosen by varying a tunable parameter of any segmentation model, and proves that with probability at least 1−α one of those masks overlaps the true object mask by more than a user-chosen IoU. The set is built from a calibration dataset by selecting the fewest parameter values that together succeed on at least 1−α of calibration queries, then removing near-duplicate masks and re-calibrating the IoU threshold. A user who trusts the guarantee can act on the set—for example, present the alternatives to a human—knowing the chance that no good mask is offered is below α. The paper demonstrates the method on agricultural fields, cells, and vehicles, where sets shrink for easy queries and expand for ambiguous ones.

What carries the argument

The engine is a set-cover conformal calibration over a grid of tunable parameter values. For each parameter value, the calibration queries where the predicted mask has IoU above the threshold are collected into a set; the algorithm finds the smallest subset of parameters whose sets together cover at least 1−α of calibration queries, and uses those parameters to generate the test query's masks. A duplicate-removal step then keeps a minimal subset of masks whose pairwise IoU exceeds a redundancy threshold, and the IoU threshold is re-calibrated to the α-quantile of per-query best IoUs, recovering a valid guarantee for the reduced set.

What would settle it

Record the maximum IoU with the ground truth among masks in the returned set for a large IID test set, using the same calibration settings. If the fraction of queries whose maximum IoU falls below the reported re-calibrated threshold exceeds α by more than finite-sample slack, the claimed coverage guarantee is false. More directly, if on the calibration set more than αn queries have IoU at or below the threshold for every parameter in the grid, Algorithm 1 cannot return a set, contradicting the claim that the procedure always provides certified sets for feasible choices.

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Extended reading notes

Core claim

The central claim, stated as Theorem 2.1, is that under IID calibration data and technical assumptions, the adaptive prediction set produced by the full algorithm satisfies a coverage guarantee: in the limit, the probability that at least one mask in the returned set reaches the re-calibrated IoU threshold is at least 1−α. In plain terms, the set contains at least one mask with high overlap to the true object at the declared level, with controlled error probability. A finite-sample variant uses a calibration split and a risk-control argument to give a non-asymptotic guarantee of the same form. The method's key design choice is to output several qualitatively different masks rather than one d

Load-bearing premise

The load-bearing premise is that the chosen parameter grid actually contains a high-IoU mask for more than 1−α of queries: if the base model cannot articulate the right answer for a query at any setting, no set built from those settings can be certified, and the algorithm fails or needs a more lenient error rate or IoU target.

Editorial extensions

If this is right

Prediction sets adapt to query difficulty: easy queries get one or two masks, ambiguous queries get more, as observed across all three datasets.
Coverage at the target level is achieved where a single best parameter value or a dilated mask cannot, because the set can represent mutually incompatible hypotheses such as merged versus split fields.
The achievable error-rate and IoU frontier quantifies the reliability ceiling of the base model; conformal prediction can certify but cannot repair a model that lacks a good mask for more than α of queries.
Removing duplicates does not destroy the guarantee: the re-calibrated IoU threshold stays near or above the original threshold in the experiments.
A finite-sample formulation preserves the guarantee without asymptotic assumptions, at the cost of possibly larger prediction sets.

Reading between the lines

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

The set-cover framing suggests that instance segmentation uncertainty is inherently combinatorial: the right confidence object is a set of mutually exclusive hypotheses, which connects to ensemble and multiple-choice prediction problems beyond segmentation.
The feasibility frontier can be read as a diagnostic: plotting the max-IoU histogram for calibration queries tells a practitioner how much of the model's failures are fixable by offering alternatives versus irreducible model error.
A natural extension would use the same machinery with diverse base models or prompts rather than one model's parameter sweep; the guarantee only requires a parameterized family of masks and a calibration sample, so the method should transfer to any such family.
Because the guarantee is distribution-dependent, applying it in deployment requires the test-time distribution to match calibration; the IID assumption is the condition a practitioner should check before relying on the declared coverage.

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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

I'll cut to the chase: the set-cover idea for instance segmentation is a genuine contribution, and the conformal theory is standard and mostly sound. The real problem is that the experiments choose the operating point (α,τ) from the same calibration data used to build the sets, so the headline coverage claim is not actually established by Theorem 2.1. That's fixable with a clean validation/calibration split, and the paper should go to review.

What's new: existing conformal segmentation methods either dilate one mask or pick a single parameter value. This paper selects a subset of tunable parameter values using a set cover, removes near-duplicates, and recalibrates the IoU threshold. That produces confidence sets with structurally different masks, which matters for field delineation and similar tasks where a single mask can be over- or under-segmented. The proofs in Appendix C are standard exchangeability arguments; under Assumptions 1, A.2–A.4 they look correct. The finite-sample version in Appendix H is a real addition, though it is not used in the experiments.

Soft spots. The stress-test note is on target. Section 3.2 picks α and τ by minimizing α and maximizing τ subject to feasibility on the calibration histograms of max IoU. Theorem 2.1 requires fixed parameters that satisfy the feasibility assumption. When the target is selected on the same data that later constructs the sets, the coverage at the selected target does not follow from the theorem. The reported numbers are single-split point estimates with no error bars, so the apparent agreement with 1−α may be partly a selection artifact. This is a localized experimental issue, not a broken proof. Fixing it requires a separate split for target selection, then a fresh calibration set for the conformal step. I would also like to see the finite-sample algorithm run, or at least error bars on the coverages.

I do not agree that the method is circular in the conformal sense. The theory is not circular; the empirical demonstration has a self-referential component, which is what the stress-test identified. The reader's conditional verdict is fair, and I am slightly more optimistic because the flaw is so clearly localized.

This paper deserves a serious referee. The algorithm is new and usable, and the main defect is an experimental design choice that can be corrected. I would cite it once the split is fixed; as is, I would still cite the method with a caveat. Good reading-group material.

Referee Report

2 major / 6 minor

Summary. This paper proposes a conformal prediction method for instance segmentation. Given an image and a pixel query, the algorithm varies a tunable parameter of a base segmentation model over a grid, identifies a small set of parameter values whose masks jointly achieve IoU > τ on at least (1−α) of the calibration data, and returns the corresponding masks as the confidence set (Algorithm 1). A post-processing step removes near-duplicate masks and recalibrates the IoU threshold θ̃ using the α-quantile of per-calibration-point best IoU scores (Algorithm 2). The main theorem (Theorem 2.1) claims asymptotic coverage P(max_{y∈C} IoU(Y_test, y) ≥ θ̃) ≥ 1−α under IID sampling and additional assumptions (A.2–A.4). A finite-sample variant based on Conformal Risk Control is given in Appendix H. Experiments on agricultural field delineation, cell segmentation, and vehicle detection report coverage close to the target 1−α and larger, more diverse prediction sets than single-parameter baselines.

Significance. The contribution is timely and potentially useful: it is among the first to construct structurally diverse instance-segmentation prediction sets (rather than dilations of a single mask) with formal conformal guarantees. The proof strategy is standard but careful, with explicit feasibility and tie-breaking assumptions, and the finite-sample CRC variant in Appendix H is a valuable addition. Code and data are released, and the empirical adaptivity results are suggestive. The principal weakness is experimental: the operating point (α, τ) is selected from the same calibration data used to build the prediction sets, so the headline claim that the method 'attains the target coverage' at the reported targets is not established by Theorem 2.1. This is fixable with a proper calibration/validation split, but it is central to the empirical claim.

major comments (2)

[§3.2, Fig. D.1; Theorem 2.1] The operating point is selected from the same calibration data used for calibration. Section 3.2 states that α and τ are chosen by 'minimizing the target error rate α while maximizing IoU threshold τ, subject to feasibility' from the calibration maximum-IoU histograms, and Table 2 reports coverage at these data-selected targets. Theorem 2.1 requires α, τ, η to be fixed before observing the calibration sample. Therefore the reported 0.797/0.835/0.843 coverages are single-split point estimates at data-dependent targets, and the 'attains target coverage' claim is not justified by the theorem. Fix: use a separate validation split to choose (α, τ), then a fresh calibration split to run Algorithm 2 with those fixed values, and report confidence intervals or repeated-split variability.
[Section 2.3, Theorem 2.1, Proof C.4] The theorem's formal event is written as max_{y∈C} IoU(Y_test, y) ≥ θ̃, but the prose interprets it as 'there exists y∈C with IoU > θ̃'. These are not equivalent when C is empty. The paper reports that 'A few sets have size zero because the model classifies the queried pixel as a non-cell' (Section 3.2), so empty sets occur in the experiments. The proof defines M(x, y, J) as a maximum over u(x, J) without specifying a convention for the empty set. Without such a convention, the theorem is either undefined or can be vacuously satisfied. Please define max over the empty set (or require C nonempty in the coverage event) and adjust the quantile calibration accordingly.

minor comments (6)

[Abstract / Section 3.2] The phrase 'attain the target coverage' is too strong given the data-dependent target selection; please qualify it as 'attain coverage for the chosen (α, τ)'.
[Table 2] Report uncertainty: the vehicle test set has only 121 pixels, so the 0.843 coverage estimate has a standard error around 0.033. Add confidence intervals or repeated-split results.
[Section 3.1] The 'feasible LTT/CRC baseline' is not actually LTT or CRC; it is an oracle that picks the best single parameter on the calibration set. Rename it to avoid implying that LTT/CRC itself was run.
[Section 2.2 / Proposition C.1] The statement 'with probability at least (1−α) asymptotically' is a lim inf guarantee; make this explicit in the main text to avoid confusion with finite-sample guarantees.
[Algorithm 3, Line 24] The arg max in the greedy ranking step does not specify a tie-breaking rule. A deterministic tie-break should be stated, consistent with Assumption A.3.
[Figure 1 / Table 2] Figure 1's caption says '80% coverage at IoU > 0.7', but Table 2 reports θ̃=0.696 for the field example. Align the numbers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the conformal coverage derivation is a standard exchangeability argument and the experimental (α,τ) selection is a non-circular statistical caveat.

full rationale

Theorem 2.1 and its proof do not reduce to their inputs. Algorithm 1 selects J by covering calibration points; coverage on a fresh test point follows from exchangeability and the quantile property of the calibration scores s_i. The proof invokes Fact 2.15(ii) from Angelopoulos et al. (2025a), a standard parameter-free result by overlapping authors, but this is independent support, not a circularity. The finite-sample algorithm is a direct application of CRC (Angelopoulos et al., 2022), likewise an independent general result. The only concern is that Section 3.2 chooses (α,τ) from the calibration max-IoU histograms ('we minimized the target error rate α while maximizing IoU threshold τ, subject to feasibility'), whereas Theorem 2.1 is stated for fixed parameters. This is a statistical validity gap in the experimental protocol—the reported test coverage at a data-dependent operating point does not follow from the theorem as stated—but it is not circular: the test set is held out, and the test coverage is not forced to equal 1−α by the calibration feasibility condition. No equation in the paper is definitionally equivalent to the claimed result.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim's input cost is mostly standard conformal machinery plus two feasibility/regularity assumptions (A.2, A.4). The main non-standard choices are the data-dependent targets α,τ and the parameter grid, which define what the guarantee can certify. No invented entities are postulated.

free parameters (4)

target error rate α = 0.2 (fields, cells), 0.1 (vehicle)
Chosen from calibration feasibility histograms (Section 3.2, Fig D.1), not fixed a priori; the coverage guarantee is stated for a pre-specified α.
target IoU threshold τ = 0.7 (fields), 0.75 (cells), 0.8 (vehicle)
Data-dependent selection; defines what counts as a 'good' mask for the guarantee.
tunable-parameter grid {t1,...,tk} = watershed T 0–1 step 0.001/0.01; cell extent −5..5 step 1; SAM index {1,2,3} × threshold step 0.05
The grid defines the hypothesis space; Assumption A.2 requires the grid to contain a good mask for >1−α of queries.
duplicate threshold η = 0.9
User-specified overlap threshold for duplicate removal; not fitted, but affects set size and re-calibrated θ~.

assumptions (5)

domain assumption Calibration and test samples are IID (Assumption 1)
Needed for exchangeability used in Prop. C.1 and Theorem 2.1 proofs (Section 2.1).
domain assumption Feasibility: P(max_j IoU(Y, f(X,t_j)) > τ) > 1−α (Assumption A.2)
If the model/parameter grid cannot produce a good mask for >1−α fraction of queries, Algorithm 1 returns an error (Section 2.2 'Not every α, τ are possible').
ad hoc to paper Fixed tie-breaking ordering in set searches (Assumption A.3)
Makes Algorithm 2's UNIQUE deterministic so J(n) converges to J*; the authors say it holds in most implementations (Appendix C.1).
ad hoc to paper Strict gap µτ(J*) > 1−α (Assumption A.4)
Needed to show J(n) → J* with probability 1; authors say it 'generally holds' with a continuous prior (Appendix C.1).
standard math Exchangeability quantile lemma (Fact 2.15 of Angelopoulos et al. 2025a) and WLLN
Used in proof of Theorem 2.1 and Lemma C.1 (Appendix C).

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Cite this review

Pith. "Pith review of Conformal Prediction Sets for Instance Segmentation." pith.science (2026). https://pith.science/paper/QG6KGB2D

@misc{pith2026260210045,
  author       = {Pith},
  title        = {Pith review of: Conformal Prediction Sets for Instance Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QG6KGB2D}},
  note         = {Machine review of arXiv:2602.10045}
}

read the original abstract

Current instance segmentation models achieve high performance on average predictions, but lack principled uncertainty quantification: their outputs are not calibrated, and there is no guarantee that a predicted mask is close to the ground truth. To address this limitation, we introduce a conformal prediction algorithm to generate adaptive confidence sets for instance segmentation. Given an image and a pixel coordinate query, our algorithm generates a confidence set of instance predictions for that pixel, with a provable guarantee for the probability that at least one of the predictions has high Intersection-Over-Union (IoU) with the true object instance mask. We apply our algorithm to instance segmentation examples in agricultural field delineation, cell segmentation, and vehicle detection. Empirically, we find that our prediction sets vary in size based on query difficulty and attain the target coverage, outperforming baselines (naive best parameter and morphological dilation-based methods). We provide versions of the algorithm with asymptotic and finite sample guarantees. Our work is the first to capture structural uncertainty in instance segmentation by constructing confidence sets of diverse segmentation predictions.

Figures

Figures reproduced from arXiv: 2602.10045 by the authors.

**Figure 1.** Example field instance segmentation queries with true masks, model softmax scores, baseline predictions, and our method’s conformal prediction sets (with IoU scores shown below each prediction). Given an image and a pixel coordinate query, our conformal algorithm generates a confidence set of instance predictions for that pixel, with a provable guarantee for the probability that at least one of the predictions has h… view at source ↗

**Figure 2.** Generating diverse predictions by varying tunable parameter T. In the field delineation example, we vary the watershed algorithm threshold T to generate multiple segmentations for each image. While a given threshold may oversegment or undersegment a specific field, another threshold often succeeds, motivating the use of prediction sets that combine them. Algorithm 1 Conformal prediction set for instance segmentat… view at source ↗

**Figure 3.** Cumulative distributions of IoUs of feasible LTT/CRC baseline predictions and our conformal prediction sets over test data points. For our conformal prediction sets, the maximum IoU over all predictions is used. In all examples, our conformal coverage for IoU > ˜θ is close to target coverage (1 − α) and greater than baseline coverage. Furthermore, the re-calibrated IoU threshold ˜θ is close to (or greater than) the … view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Distribution of conformal prediction set sizes for test data points, after removing duplicate predictions. Our algorithm constructs adaptive confidence sets that vary in size for different inputs. Tα,τ is the set of values of tunable parameter T used to generate the in…

**Figure 5.** Figure 5: Conformal prediction sets for example test queries, compared to feasible LTT/CRC baseline predictions. Our conformal sets often include masks of different sizes or shapes, capturing structural uncertainty. Most contain at least one mask with high IoU (green) with the…

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Works this paper leans on

14 extracted references · 4 linked inside Pith · cited by 1 Pith paper

[1]

Confident object detection via conformal prediction and conformal risk control: an ap- plication to railway signaling

Andéol, Léo et al. (2023). “Confident object detection via conformal prediction and conformal risk control: an ap- plication to railway signaling.” In:Conformal and Prob- abilistic Prediction with Applications. PMLR, pp. 36–

2023
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Next, define M:X × Y × Pk →[0,1] to be the function given by M(x, y, J)≡max ˆy∈u(x,J) IoU(y,ˆy) for allx∈ X, y∈ Y,andJ⊆[k]

Note that by Assumption A.3, the procedure UNIQUE is deter- ministic and hence u(·,·) is a deterministic function. Next, define M:X × Y × Pk →[0,1] to be the function given by M(x, y, J)≡max ˆy∈u(x,J) IoU(y,ˆy) for allx∈ X, y∈ Y,andJ⊆[k]. Note that M:X × Y × Pk →[0,1] is also a deterministic function. Finally let Qα(·) be a deterministic operator that tak...

2025
[10]

cov- ered

The conformal guarantee is that for a test pixel, with 80% probability, dilating the predicted mask by D= 2 pixels will result in a mask that contains the true field. ResultsThe dilation-based method results in low coverage for IoU, undersegmentation, and lack of flexibility in predictions. We visualize results for five example test points (Figure F.1). T...

2009
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Thus, we can apply Conformal Risk Control (Angelopoulos et al., 2022)

= 0< α. Thus, we can apply Conformal Risk Control (Angelopoulos et al., 2022). Our algorithm computes the smallest value of λ such that the empirical risk ˆr(λ) =1 n2 Pn1+n2 i=n1+1 li(λ) falls below the CRC threshold: ˆλ= min{λ: ˆr(λ)≤α− 1−α n2 }. For a new test point (Xtest, Ytest), let ltest(λ) =1(max ˆy∈Cλ(Xtest) IoU(Y test,ˆy)≤τ) . Then by Theorem 1 o...

2022
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In Algorithm 1, we use the greedy set cover algorithm to find a set of parameters that covers (1−α) fraction of the calibration points; analogously, in the CRC step of Algorithm 3, we add parameters from the ranked list L until we cover(1−α+ 1−α n2 )fraction of then 2 calibration points. However, one advantage of Algorithm 1 is that we can improve the gre...

2025
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We evaluate our method on 200 images with car instance labels from the Cityscapes street scene validation dataset (Cordts et al., 2016)

Vehicle detectionDetecting vehicles in street-level imagery is a central task in autonomous driving and traffic monitoring. We evaluate our method on 200 images with car instance labels from the Cityscapes street scene validation dataset (Cordts et al., 2016). We split the data into 100 calibration and 100 test images and randomly sample 20 pixels from ea...

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to compute the smallest value ˆλ∈[k] such that the first ˆλ parameters in the ranked list result in a valid conformal prediction set. The CRC method provides finite sample guarantees for the probability that for a new input Xtest (from the same distribution as the calibration ...

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Confident object detection via conformal prediction and conformal risk control: an ap- plication to railway signaling

Andéol, Léo et al. (2023). “Confident object detection via conformal prediction and conformal risk control: an ap- plication to railway signaling.” In:Conformal and Prob- abilistic Prediction with Applications. PMLR, pp. 36–

2023

[2] [2]

Next, define M:X × Y × Pk →[0,1] to be the function given by M(x, y, J)≡max ˆy∈u(x,J) IoU(y,ˆy) for allx∈ X, y∈ Y,andJ⊆[k]

Note that by Assumption A.3, the procedure UNIQUE is deter- ministic and hence u(·,·) is a deterministic function. Next, define M:X × Y × Pk →[0,1] to be the function given by M(x, y, J)≡max ˆy∈u(x,J) IoU(y,ˆy) for allx∈ X, y∈ Y,andJ⊆[k]. Note that M:X × Y × Pk →[0,1] is also a deterministic function. Finally let Qα(·) be a deterministic operator that tak...

2025

[3] [10]

cov- ered

The conformal guarantee is that for a test pixel, with 80% probability, dilating the predicted mask by D= 2 pixels will result in a mask that contains the true field. ResultsThe dilation-based method results in low coverage for IoU, undersegmentation, and lack of flexibility in predictions. We visualize results for five example test points (Figure F.1). T...

2009

[4] [12]

Thus, we can apply Conformal Risk Control (Angelopoulos et al., 2022)

= 0< α. Thus, we can apply Conformal Risk Control (Angelopoulos et al., 2022). Our algorithm computes the smallest value of λ such that the empirical risk ˆr(λ) =1 n2 Pn1+n2 i=n1+1 li(λ) falls below the CRC threshold: ˆλ= min{λ: ˆr(λ)≤α− 1−α n2 }. For a new test point (Xtest, Ytest), let ltest(λ) =1(max ˆy∈Cλ(Xtest) IoU(Y test,ˆy)≤τ) . Then by Theorem 1 o...

2022

[5] [13]

In Algorithm 1, we use the greedy set cover algorithm to find a set of parameters that covers (1−α) fraction of the calibration points; analogously, in the CRC step of Algorithm 3, we add parameters from the ranked list L until we cover(1−α+ 1−α n2 )fraction of then 2 calibration points. However, one advantage of Algorithm 1 is that we can improve the gre...

2025

[6] [14]

We evaluate our method on 200 images with car instance labels from the Cityscapes street scene validation dataset (Cordts et al., 2016)

Vehicle detectionDetecting vehicles in street-level imagery is a central task in autonomous driving and traffic monitoring. We evaluate our method on 200 images with car instance labels from the Cityscapes street scene validation dataset (Cordts et al., 2016). We split the data into 100 calibration and 100 test images and randomly sample 20 pixels from ea...

2016

[7] [39]

Segment anything

27, pp. 28151–28159. Kirillov, Alexander et al. (2023). “Segment anything.” In: Proceedings of the IEEE/CVF international conference on computer vision, pp. 4015–4026. Li, Shuo et al. (2022). “Towards pac multi-object detection and tracking.” In:arXiv preprint arXiv:2204.07482. Lovász, László (1975). “On the ratio of optimal integral and fractional covers...

arXiv 2023

[8] [49]

Reducibility among Combina- torial Problems

Karp, Richard M. (1972). “Reducibility among Combina- torial Problems.” In:Complexity of Computer Computa- tions: Proceedings of a symposium on the Complexity of Computer Computations. Ed. by Raymond E. Miller, James W. Thatcher, and Jean D. Bohlinger. Boston, MA: Springer US, pp. 85–103.ISBN: 978-1-4684-2001-2.DOI: 10.1007/978-1-4684-2001-2_9 .URL: https...

doi:10.1007/978-1-4684-2001-2_9 1972