### Abstract

The localization receiver operating characteristic (LROC) curve is a standard method to quantify performance for the task of detecting and locating a signal. This curve is generalized to arbitrary detection/ estimation tasks to give the estimation ROC (EROC) curve. For a two-alternative forced-choice study, where the observer must decide which of a pair of images has the signal and then estimate parameters pertaining to the signal, it is shown that the average value of the utility on those image pairs where the observer chooses the correct image is an estimate of the area under the EROC curve (AEROC). The ideal LROC observer is generalized to the ideal EROC observer, whose EROC curve lies above those of all other observers for the given detection/ estimation task. When the utility function is nonnegative, the ideal EROC observer is shown to share many mathematical properties with the ideal observer for the pure detection task. When the utility function is concave, the ideal EROC observer makes use of the posterior mean estimator. Other estimators that arise as special cases include maximum a posteriori estimators and maximum-likelihood estimators.

Original language | English (US) |
---|---|

Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |

Volume | 24 |

Issue number | 12 |

DOIs | |

State | Published - 2007 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Computer Vision and Pattern Recognition

### Cite this

**Estimation receiver operating characteristic curve and ideal observers for combined detection/estimation tasks.** / Clarkson, Eric W.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Estimation receiver operating characteristic curve and ideal observers for combined detection/estimation tasks

AU - Clarkson, Eric W

PY - 2007

Y1 - 2007

N2 - The localization receiver operating characteristic (LROC) curve is a standard method to quantify performance for the task of detecting and locating a signal. This curve is generalized to arbitrary detection/ estimation tasks to give the estimation ROC (EROC) curve. For a two-alternative forced-choice study, where the observer must decide which of a pair of images has the signal and then estimate parameters pertaining to the signal, it is shown that the average value of the utility on those image pairs where the observer chooses the correct image is an estimate of the area under the EROC curve (AEROC). The ideal LROC observer is generalized to the ideal EROC observer, whose EROC curve lies above those of all other observers for the given detection/ estimation task. When the utility function is nonnegative, the ideal EROC observer is shown to share many mathematical properties with the ideal observer for the pure detection task. When the utility function is concave, the ideal EROC observer makes use of the posterior mean estimator. Other estimators that arise as special cases include maximum a posteriori estimators and maximum-likelihood estimators.

AB - The localization receiver operating characteristic (LROC) curve is a standard method to quantify performance for the task of detecting and locating a signal. This curve is generalized to arbitrary detection/ estimation tasks to give the estimation ROC (EROC) curve. For a two-alternative forced-choice study, where the observer must decide which of a pair of images has the signal and then estimate parameters pertaining to the signal, it is shown that the average value of the utility on those image pairs where the observer chooses the correct image is an estimate of the area under the EROC curve (AEROC). The ideal LROC observer is generalized to the ideal EROC observer, whose EROC curve lies above those of all other observers for the given detection/ estimation task. When the utility function is nonnegative, the ideal EROC observer is shown to share many mathematical properties with the ideal observer for the pure detection task. When the utility function is concave, the ideal EROC observer makes use of the posterior mean estimator. Other estimators that arise as special cases include maximum a posteriori estimators and maximum-likelihood estimators.

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U2 - 10.1364/JOSAA.24.000B91

DO - 10.1364/JOSAA.24.000B91

M3 - Article

VL - 24

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 12

ER -