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Kandinsky Conformal Prediction: Efficient Calibration of Image Segmentation Algorithms
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Proposes Kandinsky calibration, which clusters spatially similar pixels of a segmentation network and pools their conformal non-conformity scores, giving an intermediate between imagewise and pixelwise conformal calibration that is more data-efficient in low-data regimes.
Problem
Inductive conformal prediction for image segmentation requires many calibration images for pixelwise (conditional) calibration, while imagewise (marginal) calibration is miscalibrated per pixel; calibration is hard when labeled medical data are scarce.
Approach
Cluster pixel locations by similarity of their non-conformity curves (via k-means, genetic-algorithm annuli, or Fourier concentric clustering), pool non-conformity scores within each cluster, and use the cluster-specific quantile curve for prediction sets, exploiting spatial correlation of pixel classifiers.
Key results
- On MS-COCO with 100 calibration images, Kandinsky methods (GenAnn 0.068, FCC-Ann 0.060) beat pixelwise (0.131) and imagewise (0.091) mean coverage error.
- On Decathlon-S (27 patients), GenAnn achieves 0.152 vs. 0.249 for pixelwise and 0.175 for imagewise calibration.
- With 20,000 MS-COCO calibration images, pixelwise calibration is best (0.055), with Kandinsky methods close behind (0.064-0.067).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use pixelwise calibration instead of Kandinsky calibration | U-Net segmentation · MS-COCO-XL | mean coverage error: 0.055 vs 0.064 | Helped |
| Use Kandinsky calibration instead of pixelwise calibration | U-Net segmentation · MS-COCO-S | mean coverage error: 0.131 vs 0.060 | Helped |
| Use Kandinsky calibration instead of imagewise calibration | U-Net segmentation · MS-COCO-S | mean coverage error: 0.091 vs 0.060 | Helped |
| Use Kandinsky calibration instead of pixelwise calibration | U-Net segmentation · Decathlon-L | mean coverage error: 0.217 vs 0.145 | Helped |
| Use Kandinsky calibration instead of imagewise calibration | U-Net segmentation · Decathlon-L | mean coverage error: 0.177 vs 0.145 | Helped |
| Use Kandinsky calibration instead of pixelwise calibration | U-Net segmentation · Decathlon-S | mean coverage error: 0.249 vs 0.152 | Helped |
| Use Kandinsky calibration instead of imagewise calibration | U-Net segmentation · Decathlon-S | mean coverage error: 0.175 vs 0.152 | Helped |
| Use GenAnn or FCC-Ann rather than K-means clustering | Kandinsky calibration · MS-COCO-S | mean coverage error: 0.086 vs 0.068; 0.086 vs 0.060 | Helped |
| Use k-means clustering rather than GenAnn or FCC-Ann | Kandinsky calibration · Decathlon-L | mean coverage error: 0.145 vs 0.150; 0.145 vs 0.152 | Helped |
| Use GenAnn clustering rather than K-means or FCC-Ann | Kandinsky calibration · Decathlon-S | mean coverage error: 0.152 vs 0.168; 0.152 vs 0.165 | Helped |
Surprising findings
- With 20,000 calibration images, pixelwise calibration slightly outperforms all Kandinsky methods, so the benefit is confined to low-data regimes.
- Imagewise calibration performs worse than pixelwise in the large-data regime because it averages over pixels.
Limitations
- Clustering prior must be specified by humans and depends on the data and task.
- Concentric circle/ellipse shapes do not generalize to all tasks; numerical methods may not handle all geometric priors.
- Only pixelwise coverage with a single non-conformity score (1 - f_Y) was studied; other scoring functions left to future work.
Experimental setup
Datasets: MS-COCO Medical Decathlon (Pancreas)
Benchmarks: MS-COCO Medical Decathlon Pancreas
Metrics: coverage error (CE20) mean coverage error with quantiles
Baselines: pixelwise calibration imagewise calibration k-means clustering calibration
Builds on: inductive conformal prediction differential evolution k-means clustering
Closest papers by meaning
- Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction (ICML 2025 · similarity 0.84)
- Self-Calibrating Conformal Prediction (NeurIPS 2024 · similarity 0.82)
- GapMatch: Bridging Instance and Model Perturbations for Enhanced Semi-Supervised Medical Image Segmentation (AAAI 2025 · similarity 0.82)
- Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage (ICML 2025 · similarity 0.82)
- Divide et Calibra: Multiclass Local Calibration via Vector Quantization (NeurIPS 2026 · similarity 0.82)
- Split conformal classification with unsupervised calibration (NeurIPS 2025 · similarity 0.82)
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