Continuous Dice Coefficient: a Method for Evaluating Probabilistic Segmentations

Objective Overlapping measures are often utilized to quantify the similarity between two binary regions. However, modern segmentation algorithms output a probability or confidence map with continuous values in the zero-to-one interval. Moreover, these binary overlapping measures are biased to structure’s size. Addressing these challenges is the objective of this work.

Methods We extend the definition of the classical Dice coefficient (DC) overlap to facilitate the direct comparison of a ground truth binary image with a probabilistic map. We call the extended method continuous Dice coefficient (cDC) and show that 1) cDC ≤1 and cDC = 1 if-and-only-if the structures’ overlap is complete, and; 2) cDC is monotonically decreasing with the amount of overlap. We compare the classical DC and the cDC in a simulation of partial volume effects that incorporates segmentations of common targets for deep-brain-stimulation. Lastly, we investigate the cDC for an automatic segmentation of the subthalamic-nucleus.

Results Partial volume effect simulation on thalamus (large structure) resulted with DC and cDC averages (SD) of 0.98 (0.006) and 0.99 (0.001), respectively. For subthalamic-nucleus (small structure) DC and cDC were 0.86 (0.025) and 0.97 (0.006), respectively. The DC and cDC for automatic STN segmentation were 0.66 and 0.80, respectively.

Conclusion The cDC is well defined for probabilistic segmentation, less biased to structure’s size and more robust to partial volume effects in comparison to DC. Significance: The proposed method facilitates a better evaluation of segmentation algorithms. As a better measurement tool, it opens the door for the development of better segmentation methods.