Optimization for Medical Image Segmentation: Theory and Practice When Evaluating With Dice Score or Jaccard Index

Area of Science:

• Medical Imaging
• Computer Vision
• Machine Learning

Background:

• Dice score and Jaccard index are standard metrics for segmentation performance.
• Metric-sensitive losses (soft Dice, soft Jaccard) exist but per-pixel losses (cross-entropy) are commonly used.
• This leads to a discrepancy where the training objective doesn't match the evaluation metric.

Purpose of the Study:

• To theoretically investigate the relationship between metric-sensitive loss functions.
• To question the effectiveness of weighted cross-entropy for optimizing Dice and Jaccard indices.
• To empirically validate the superiority of metric-sensitive losses over cross-entropy.

Main Methods:

• Theoretical analysis of metric-sensitive loss functions.
• Investigation of weighted cross-entropy's ability to optimize Dice and Jaccard indices.
• Empirical validation on six diverse medical segmentation tasks.

Main Results:

• Dice score and Jaccard index show strong relative and absolute approximation.
• Tversky loss approximation worsens with deviation from soft Dice.
• Metric-sensitive losses consistently outperform cross-entropy for Dice/Jaccard evaluation.

Conclusions:

• Metric-sensitive losses are superior to cross-entropy for optimizing Dice and Jaccard indices in medical segmentation.
• This superiority holds across multi-class settings, object sizes, and foreground/background ratios.
• Wider adoption of metric-sensitive losses is encouraged for relevant medical segmentation tasks.