Siemens Corporate Research, Princeton, NJ 08540 USA.
IEEE Trans Med Imaging. 2010 Feb;29(2):375-86. doi: 10.1109/TMI.2009.2031840.
Detection of multiple lesions in images is a medically important task and free-response receiver operating characteristic (FROC) analyses and its variants, such as alternative FROC (AFROC) analyses, are commonly used to quantify performance in such tasks. However, ideal observers that optimize FROC or AFROC performance metrics have not yet been formulated in the general case. If available, such ideal observers may turn out to be valuable for imaging system optimization and in the design of computer aided diagnosis techniques for lesion detection in medical images. In this paper, we derive ideal AFROC and FROC observers. They are ideal in that they maximize, amongst all decision strategies, the area, or any partial area, under the associated AFROC or FROC curve. Calculation of observer performance for these ideal observers is computationally quite complex. We can reduce this complexity by considering forms of these observers that use false positive reports derived from signal-absent images only. We also consider a Bayes risk analysis for the multiple-signal detection task with an appropriate definition of costs. A general decision strategy that minimizes Bayes risk is derived. With particular cost constraints, this general decision strategy reduces to the decision strategy associated with the ideal AFROC or FROC observer.
图像中多病灶的检测是一项重要的医学任务，自由响应接收器操作特性（FROC）分析及其变体，如替代 FROC（AFROC）分析，通常用于量化此类任务中的性能。然而，在一般情况下，尚未制定出优化 FROC 或 AFROC 性能指标的理想观测器。如果有这样的理想观测器，它们可能会对成像系统优化和用于医学图像中病灶检测的计算机辅助诊断技术的设计很有价值。在本文中，我们推导出理想的 AFROC 和 FROC 观测器。它们是理想的，因为它们在所有决策策略中最大化了与相关的 AFROC 或 FROC 曲线下的面积或任何部分面积。计算这些理想观测器的观测器性能在计算上非常复杂。我们可以通过仅考虑使用信号缺失图像中得出的假阳性报告的这些观测器的形式来降低这种复杂性。我们还考虑了具有适当成本定义的多信号检测任务的贝叶斯风险分析。推导出了一种最小化贝叶斯风险的通用决策策略。在特定的成本约束下，这个通用的决策策略会简化为与理想的 AFROC 或 FROC 观测器相关的决策策略。
