Estimation receiver operating characteristic curve and ideal observers for combined detection/estimation tasks

Area of Science:

• Medical Imaging and Signal Processing
• Statistical Decision Theory

Background:

• The localization receiver operating characteristic (LROC) curve is a standard metric for signal detection and localization performance.
• Generalizing LROC to arbitrary detection/estimation tasks is crucial for comprehensive performance evaluation.

Purpose of the Study:

• To introduce and define the estimation ROC (EROC) curve as a generalization of the LROC curve.
• To establish a method for estimating the area under the EROC curve (AEROC) in two-alternative forced-choice tasks.
• To define and characterize the ideal EROC observer.

Main Methods:

• Generalizing the LROC curve to the EROC curve for detection/estimation tasks.
• Deriving the relationship between average utility on correct choices and AEROC in two-alternative forced-choice studies.
• Defining the ideal EROC observer and analyzing its mathematical properties.

Main Results:

• The average utility on correctly identified image pairs is shown to be an estimate of AEROC.
• The ideal EROC observer is defined, generalizing the ideal LROC observer.
• Under specific utility function conditions (nonnegative, concave), the ideal EROC observer exhibits properties similar to the ideal detection observer and utilizes specific estimators like posterior mean, MAP, and ML.

Conclusions:

• The EROC curve provides a unified framework for evaluating detection and estimation tasks.
• The proposed method offers a practical way to estimate task performance (AEROC).
• The ideal EROC observer serves as a benchmark for optimal performance in complex detection/estimation scenarios.