[论文解读] Continuous Dice Coefficient: a Method for Evaluating Probabilistic Segmentations

Reuben R. Shamir, Yuval Duchin+3 more|arXiv (Cornell University)|Jun 26, 2019

Neurological disorders and treatments被引用 10

一句话总结

本文提出了连续Dice系数（cDC），这是一种新颖的评估指标，将经典的Dice系数扩展至直接比较概率分割图（取值范围在0到1之间的连续值）与二值真值。cDC在理论上定义良好，取值范围为0到1，重叠减少时单调递减，且在部分体积效应下表现出优于经典Dice系数的鲁棒性，并降低了对结构大小的偏差，该结论已在丘脑和下丘脑核团分割任务中得到验证。

ABSTRACT

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 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 is less or equal to 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-brainstimulation. 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 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.

研究动机与目标

• 解决将经典二值重叠度量（如Dice系数）应用于概率分割输出时的局限性。
• 减少因结构大小差异导致的分割评估偏差。
• 开发一种连续且数学上严谨的指标，直接评估置信度图与二值真值。
• 提高医学影像中分割算法评估的可靠性，尤其是在存在部分体积效应的情况下。
• 通过提供更精确的评估信号，支持深度学习模型的更好训练与优化。

提出的方法

• cDC通过在连续概率图上积分，而非二值区域，扩展了经典Dice系数。
• 其重叠定义为预测概率图与真值二值图乘积的积分，归一化为预测图与真值图之和。
• 该方法确保cDC ≤ 1，且当且仅当预测图与真值完全重叠时cDC = 1。
• cDC随预测与真值区域之间不一致或错位程度的增加而单调递减。
• 该公式源自离散Dice系数的连续极限，保留了关键理论性质。
• 该方法通过模拟部分体积效应以及对下丘脑核团和丘脑的真实分割任务进行了验证。

实验结果

研究问题

• RQ1 能否构建一种连续扩展的Dice系数，使其在比较概率图与二值真值时保持有界性与可解释性？
• RQ2 与经典Dice系数相比，cDC在部分体积效应下的表现如何？
• RQ3 cDC在多大程度上减少了对较大解剖结构在分割评估中的偏差？
• RQ4 cDC是否能作为神经影像中基于深度学习的分割模型更鲁棒、更可靠的评估指标？
• RQ5 cDC能否作为训练分割网络的更优优化目标？

主要发现

• 在丘脑（大结构）的部分体积效应模拟中，经典Dice系数平均为0.98（标准差0.006），而cDC平均为0.99（标准差0.001），显示出更高的稳定性。
• 对于下丘脑核团（小结构），经典Dice系数为0.86（标准差0.025），而cDC达到0.97（标准差0.006），表明对小结构的偏差显著降低。
• 在下丘脑核团的自动分割中，经典Dice系数为0.66，而cDC为0.80，显示出评估结果间存在显著差距。
• cDC在抗部分体积效应方面始终优于经典Dice系数，且对结构大小的敏感性更低。
• cDC的理论性质——有界性与单调性——得以保持，证实其作为连续评估指标的合理性。
• 结果表明，cDC是医学图像分析中评估概率分割输出更可靠、更具信息量的指标。