On Image Segmentation With Noisy Labels: Characterization and Volume Properties of the Optimal Solutions to Accuracy and Dice

TL;DR

This paper analyzes the behavior of Accuracy and Dice metrics in medical image segmentation with noisy labels, revealing how optimal solutions' volumes deviate from the true target and comparing their properties.

Contribution

It provides theoretical characterization and experimental validation of the volume properties of optimal solutions under noisy labels for Accuracy and Dice metrics.

Findings

Solution volumes can significantly deviate from the target volume.

Accuracy solutions have volume less than or equal to Dice solutions.

Optimal solutions for both metrics coincide under volume constraints.

Abstract

We study two of the most popular performance metrics in medical image segmentation, Accuracy and Dice, when the target labels are noisy. For both metrics, several statements related to characterization and volume properties of the set of optimal segmentations are proved, and associated experiments are provided. Our main insights are: (i) the volume of the solutions to both metrics may deviate significantly from the expected volume of the target, (ii) the volume of a solution to Accuracy is always less than or equal to the volume of a solution to Dice and (iii) the optimal solutions to both of these metrics coincide when the set of feasible segmentations is constrained to the set of segmentations with the volume equal to the expected volume of the target.