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

Xin He, Eric C. Frey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2010
Subtitle of host publicationImage Perception, Observer Performance, and Technology Assessment
StatePublished - 2010
Externally publishedYes
EventMedical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment - San Diego, CA, United States
Duration: Feb 17 2010Feb 18 2010

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2010: Image Perception, Observer Performance, and Technology Assessment
Country/TerritoryUnited States
CitySan Diego, CA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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