Efficient Conformal Volumetry for Template-Based Segmentation

Matt Y. Cheung; Ashok Veeraraghavan; Guha Balakrishnan

eess.IVFeb 28, 2026

Efficient Conformal Volumetry for Template-Based Segmentation

Authors: Matt Y. Cheung, Ashok Veeraraghavan, Guha Balakrishnan

Organizations: Department of Electrical & Computer Engineering Rice University Houston, TX 77005, USA

Abstract

Template-based segmentation, a widely used paradigm in medical imaging, propagates anatomical labels via deformable registration from a labeled atlas to a target image, and is often used to compute volumetric biomarkers for downstream decision-making. While conformal prediction (CP) provides finite-sample valid intervals for scalar metrics, existing segmentation-based uncertainty quantification (UQ) approaches either rely on learned model features, often unavailable in classic template-based pipelines, or treat the registration process as a black box, resulting in overly conservative intervals when applied directly in output space. We introduce ConVOLT, a CP framework that achieves efficient volumetric UQ by conditioning calibration on properties of the estimated deformation field from template-based segmentation. ConVOLT calibrates a learned volumetric scaling factor from deformation space features. We evaluate ConVOLT on template-based segmentation tasks involving global, regional, and label volumetry across multiple datasets and registration methods. ConVOLT achieves target coverage while producing substantially tighter intervals than output-space conformal baselines. Our work paves way to exploit the registration process for efficient UQ in medical imaging pipelines.

Figures & tables

Figure 1: Overview of ConVOLT. We show a standard template-based segmentation pipeline for case $i$ (black) where a moving image is registered to a fixed image, resulting in a deformation field. The fixed labels are warped to compute predicted labels and volumes $\widehat{Y}^{0}_{i,l}$ on the moved image. ConVOLT (blue) trains a label-specific regressor on the training dataset $D_{tr}$ with statistical features extracted from the deformation field features to predict a multiplicative scaling factor $\widehat{\beta}_{i,l}$ . The scaling factor is conformalized using the calibration dataset $D_{cal}$ to attain valid prediction intervals.

Dataset	Method	Coverage	Interval Size (mL)	Coverage	Interval Size (mL)
		Demons		VoxelMorph
ThoraxCBCT	CQR	0.90±0.14	2707±951	0.91±0.15	2355±830
	ConVOLT	0.93±0.12	1222±357	0.93±0.14	2354±1018
	LCP	0.91±0.13	4631±986	0.91±0.15	2400±542
	SCP	0.91±0.13	4631±986	0.91±0.15	2400±542
NLST	CQR	0.91±0.06	496±84	0.91±0.06	446±117

Table 1: ConVOLT achieves high efficiency compared to baselines for global volume guarantees. For

\alpha=0.1

, we show interval size and coverage (Mean

\pm

STD) for SCP, CQR, LCP, and ConVOLT. While ConVOLT performs well on the majority of benchmarks, it achieves slightly worse/comparable performance on NLST with Demons and ThoraxCBCT with VoxelMorph.

Dataset	Agg	Method	Coverage	Interval Size (mL)	Coverage	Interval Size (mL)
			Demons		VoxelMorph
ThoraxCBCT	max	CQR	0.91±0.14	1381±362	0.92±0.13	1148±273
	max	ConVOLT	0.92±0.14	1117±146	0.95±0.10	1128±295
	$Q_{0.9}$	CQR	0.91±0.14	1139±187	0.92±0.14	898±154
	$Q_{0.9}$	ConVOLT	0.92±0.14	743±111	0.95±0.11	822±176
NLST	max	CQR	0.91±0.05	670±39	0.91±0.05	376±34

Table 2: ConVOLT achieves high efficiency compared to CQR for regional guarantees. For

\alpha=0.1

, we show interval size and coverage (Mean

\pm

STD) for CQR (best performing baseline) and ConVOLT. While ConVOLT performs well on the majority of benchmarks, it has noticeably worse performance on NLST.

Figure 2: ConVOLT achieves high efficiency compared to CQR for label volume guarantees. For $\alpha=0.1$ , we show interval size inflation of CQR (best performing baseline) in % for each label in OASIS with ConVOLT as the baseline. We find that ConVOLT achieves higher efficiency on the majority of labels.

Figure 3: Coefficient magnitudes explain ConVOLT’s efficiency improvements. We show Mean $\pm$ STD of absolute ridge coefficients for features across 100 random calibration-test splits. Large and stable magnitudes indicate features are consistently used to predict multiplicative correction, while small and unstable magnitudes indicate the limited predictive value of features and explains weaker performance.

		Demons		VoxelMorph
Dataset	Ablation	Coverage	Inflation (%)	Coverage	Inflation (%)
ThoraxCBCT	Additive	0.93±0.13	41.4±56.1	0.94±0.14	2.8±60.4
	No Features	0.91±0.14	93.4±77.3	0.91±0.15	-22.2±38.5
	No Learning	0.91±0.13	218.1±108.4	0.90±0.14	-7.1±45.5
	Global Features	0.92±0.14	73.8±32.9	0.95±0.11	65.7±57.8
NLST	Additive	0.91±0.06	3.3±26.3	0.91±0.06	0.2±28.5

Table 3: Multiplicative modeling, learned ratios, and localized features improve ConVOLT efficiency. We report interval inflation (%) relative to ConVOLT when replacing multiplicative modeling with additive corrections, removing learning or features, or using global instead of local deformation features.

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Quantifying Volumetric Risk: Class-Aware Asymmetric Weighted Conformal Prediction for 3D Medical Image Segmentation

Shadi Alijani, Fereshteh Aghaee Meibodi, Homayoun Najjaran

University of Victoria, 800 Finnerty Road, Victoria, BC, Canada

Conformal Prediction Segmentation Uncertainty Estimation Weighted Conformal Prediction 3D Medical Image Segmentation Brain Tumor Segmentation

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Reliable volumetric segmentation is critical for clinical diagnostics, yet foundation models such as MedSAM remain deterministic and lack calibrated uncertainty under distribution shift. Existing conformal prediction methods offer statistical guarantees but are frequently applied in 2D and assume symmetric error distributions, so they do not capture the class-specific biases that arise in 3D multi-class segmentation. We propose Class-Aware Asymmetric Weighted Conformal Prediction (CA-WCP), which combines latent-space density-ratio weighting for covariate shift with directional quantiles for the lower and upper volume bounds, and scales each bound by a class-specific asymmetry factor derived from validation-set false-positive and false-negative rates. We prove that CA-WCP retains the weighted-exchangeability marginal coverage guarantee for every class, and we evaluate it on 3D brain tumor segmentation (BraTS 2020) and on a synthetic multi-organ CT benchmark constructed under covariate shift. On both benchmarks the 95% Clopper--Pearson interval for the observed coverage of CA-WCP contains the nominal 90% level for every semantic class, while interval width is reduced by 8--14% relative to symmetric weighted conformal prediction. We further encode the calibrated intervals into structured prompts for a multimodal large language model to produce uncertainty-conditioned radiology reports, linking distribution-shift-aware uncertainty quantification to interpretable clinical communication.

Abstract

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