Binary ROC curve and three-class 2-D ROC surface

Xin He; Eric C. Frey

doi:10.1117/12.844593

3 March 2010 Binary ROC curve and three-class 2-D ROC surface

Xin He, Eric C. Frey

Proceedings Volume 7627, Medical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment; 762710 (2010) https://doi.org/10.1117/12.844593
Event: SPIE Medical Imaging, 2010, San Diego, California, United States

Abstract

In this work, we compared the binary ROC curve and the 2-D three-class ROC surface. We found that the 2-D three-class ROC surface shares most of the properties of the binary ROC curve. In particular, the curve (or surface) has the same DOF as the as the decision rule that is used to generate it; the curve (or surface) contains all the optimal operating points under various decision criteria (note that for three-class, the equal error utility assumption is assumed, same below); different decision criteria result in the same ROC curve (or surface) by considering all the possible prior information; ROC curve (or surface) uniquely corresponds to one pair (or triplet) of likelihood ratio distributions, assuming such a pair (or triplet) exists; the ROC curve (or surface) is concave; and the ROC curve (or surface) provides graphic information as well as figure-of-merit for task performance. We thus conclude that that the 2-D ROC surface may be preferable as a starting point for comparing systems used to perform 3-class diagnostic tasks.

Citation Download Citation

Xin He and Eric C. Frey "Binary ROC curve and three-class 2-D ROC surface", Proc. SPIE 7627, Medical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment, 762710 (3 March 2010); https://doi.org/10.1117/12.844593

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