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Class and Region-Adaptive Constraints for Network Calibration

Balamurali Murugesan, Julio Silva-Rodriguez, Ismail Ben Ayed, Jose Dolz

TL;DR

The paper addresses miscalibration in semantic segmentation by introducing CRaC, an approach that learns class- and region-wise penalties during training using an Augmented Lagrangian framework. It extends prior works by replacing a uniform penalty with per-class, per-region weights and solving the constrained objective via ALM, enabling adaptive penalty learning through outer and inner iterations and updates guided by a penalty function $P(z,\rho,\lambda)$. The authors demonstrate that CRaC achieves strong segmentation performance while improving calibration on two medical segmentation benchmarks (ACDC and FLARE) across two backbones (UNet and nnUNet), with favorable Friedman ranks. The work offers a practical, automation-friendly calibration strategy with code available at the associated repository, potentially enabling more reliable uncertainty estimates in safety-critical segmentation applications.

Abstract

In this work, we present a novel approach to calibrate segmentation networks that considers the inherent challenges posed by different categories and object regions. In particular, we present a formulation that integrates class and region-wise constraints into the learning objective, with multiple penalty weights to account for class and region differences. Finding the optimal penalty weights manually, however, might be unfeasible, and potentially hinder the optimization process. To overcome this limitation, we propose an approach based on Class and Region-Adaptive constraints (CRaC), which allows to learn the class and region-wise penalty weights during training. CRaC is based on a general Augmented Lagrangian method, a well-established technique in constrained optimization. Experimental results on two popular segmentation benchmarks, and two well-known segmentation networks, demonstrate the superiority of CRaC compared to existing approaches. The code is available at: https://github.com/Bala93/CRac/

Class and Region-Adaptive Constraints for Network Calibration

TL;DR

The paper addresses miscalibration in semantic segmentation by introducing CRaC, an approach that learns class- and region-wise penalties during training using an Augmented Lagrangian framework. It extends prior works by replacing a uniform penalty with per-class, per-region weights and solving the constrained objective via ALM, enabling adaptive penalty learning through outer and inner iterations and updates guided by a penalty function . The authors demonstrate that CRaC achieves strong segmentation performance while improving calibration on two medical segmentation benchmarks (ACDC and FLARE) across two backbones (UNet and nnUNet), with favorable Friedman ranks. The work offers a practical, automation-friendly calibration strategy with code available at the associated repository, potentially enabling more reliable uncertainty estimates in safety-critical segmentation applications.

Abstract

In this work, we present a novel approach to calibrate segmentation networks that considers the inherent challenges posed by different categories and object regions. In particular, we present a formulation that integrates class and region-wise constraints into the learning objective, with multiple penalty weights to account for class and region differences. Finding the optimal penalty weights manually, however, might be unfeasible, and potentially hinder the optimization process. To overcome this limitation, we propose an approach based on Class and Region-Adaptive constraints (CRaC), which allows to learn the class and region-wise penalty weights during training. CRaC is based on a general Augmented Lagrangian method, a well-established technique in constrained optimization. Experimental results on two popular segmentation benchmarks, and two well-known segmentation networks, demonstrate the superiority of CRaC compared to existing approaches. The code is available at: https://github.com/Bala93/CRac/
Paper Structure (10 sections, 12 equations, 2 figures, 2 tables)

This paper contains 10 sections, 12 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Background
  4. Class and region-wise penalties
  5. The proposed class and region adaptive solution
  6. Experiments
  7. Conclusion.
  8. Penalty functions for ALM: axioms
  9. Additional details on evaluation metrics
  10. Additional results: logit distributions

Figures (2)

  • Figure 1: Instability of NACL fine-tuning. Discriminative (left) vs. calibration performance (right) as a function of $\lambda$ in NACL murugesan2023trust.
  • Figure 2: Distribution of logit values. A desirable logit distribution exhibits lower winner logit magnitudes, which facilitate the training of a well-calibrated model, while pushing the remaining logit values to a considerable distance, and thus preserve a high discriminative power. An interesting observation from this figure is that, while NACL seems to generate desirable logit distributions for one dataset (FLARE), it may require fine-tuning of the $\lambda$ hyperparameter. In contrast, CRaC integrates an explicit mechanism to learn these values automatically, which facilitates a better compromise between segmentation and calibration.