# Kandinsky Conformal Prediction: Efficient Calibration of Image Segmentation Algorithms

arXiv: https://arxiv.org/abs/2311.11837 · HTML: https://mlsanity.com/paper/2311.11837/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 20 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [The Calibration Generalization Gap](https://mlsanity.com/paper/2210.01964/) (2022)
- [Confidence Calibration for Object Detection and Segmentation](https://mlsanity.com/paper/2202.12785/) (2022)
- [A Theoretical and Practical Framework for Evaluating Uncertainty Calibration in Object Detection](https://mlsanity.com/paper/2309.00464/) (2023)

## Built on by (most cited first, 14 of 14)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage](https://mlsanity.com/paper/2502.17264/) (2025)
- [Conformal Risk Control for Semantic Uncertainty Quantification in Computed Tomography](https://mlsanity.com/paper/2503.00136/) (2025)
- [A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentation](https://mlsanity.com/paper/2411.16370/) (2024)
- [WQLCP: Weighted Adaptive Conformal Prediction for Robust Uncertainty Quantification Under Distribution Shifts](https://mlsanity.com/paper/2505.19587/) (2025)
- [Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks](https://mlsanity.com/paper/2506.05434/) (2025)
- [ConformalSAM: Unlocking the Potential of Foundational Segmentation Models in Semi-Supervised Semantic Segmentation with Conformal Prediction](https://mlsanity.com/paper/2507.15803/) (2025)
- [COMPASS: Robust Feature Conformal Prediction for Medical Segmentation Metrics](https://mlsanity.com/paper/2509.22240/) (2025)
- [CONSIGN: Conformal Segmentation Informed by Spatial Groupings via Decomposition](https://mlsanity.com/paper/2505.14113/) (2025)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [Class Adaptive Conformal Training](https://mlsanity.com/paper/2601.09522/) (2026)
- [Trustworthy Endoscopic Super-Resolution](https://mlsanity.com/paper/2604.18001/) (2026)
- [ConRad: Efficient Conformal Prediction for Radiomics](https://mlsanity.com/paper/2607.08084/) (2026)
- [View-Structured Conformal Prediction for 3D Gaussian Splatting](https://mlsanity.com/paper/2609.10307/) (2026)

## Abstract (arXiv)

Image segmentation algorithms can be understood as a collection of pixel classifiers, for which the outcomes of nearby pixels are correlated. Classifier models can be calibrated using Inductive Conformal Prediction, but this requires holding back a sufficiently large calibration dataset for computing the distribution of non-conformity scores of the model's predictions. If one only requires only marginal calibration on the image level, this calibration set consists of all individual pixels in the images available for calibration. However, if the goal is to attain proper calibration for each individual pixel classifier, the calibration set consists of individual images. In a scenario where data are scarce (such as the medical domain), it may not always be possible to set aside sufficiently many images for this pixel-level calibration. The method we propose, dubbed ``Kandinsky calibration'', makes use of the spatial structure present in the distribution of natural images to simultaneously calibrate the classifiers of ``similar'' pixels. This can be seen as an intermediate approach between marginal (imagewise) and conditional (pixelwise) calibration, where non-conformity scores are aggregated over similar image regions, thereby making more efficient use of the images available for calibration. We run experiments on segmentation algorithms trained and calibrated on subsets of the public MS-COCO and Medical Decathlon datasets, demonstrating that Kandinsky calibration method can significantly improve the coverage. When compared to both pixelwise and imagewise calibration on little data, the Kandinsky method achieves much lower coverage errors, indicating the data efficiency of the Kandinsky calibration.