### Abstract

Shannon information (SI) and the ideal-observer receiver operating characteristic (ROC) curve are two different methods for analyzing the performance of an imaging system for a binary classification task, such as the detection of a variable signal embedded within a random background. In this work we describe a new ROC curve, the Shannon information receiver operator curve (SIROC), that is derived from the SI expression for a binary classification task. We then show that the ideal-observer ROC curve and the SIROC have many properties in common, and are equivalent descriptions of the optimal performance of an observer on the task. This equivalence is described mathematically by an integral transform that maps the ideal-observer ROC curve onto the SIROC. This then leads to an integral transform relating the minimum probability of error, as a function of the odds against a signal, to the conditional entropy, as a function of the same variable. This last relation then gives us the complete mathematical equivalence between ideal-observer ROC analysis and SI analysis of the classification task for a given imaging system.We also find that there is a close relationship between the area under the ideal-observer ROC curve, which is often used as a figure of merit for imaging systems and the area under the SIROC. Finally, we show that the relationships between the two curves result in new inequalities relating SI to ROC quantities for the ideal observer.

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

Pages (from-to) | 1288-1301 |

Number of pages | 14 |

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

Volume | 32 |

Issue number | 7 |

DOIs | |

State | Published - 2015 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Electronic, Optical and Magnetic Materials
- Computer Vision and Pattern Recognition

### Cite this

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

*32*(7), 1288-1301. https://doi.org/10.1364/JOSAA.32.001288

**Shannon information and ROC analysis in imaging.** / Clarkson, Eric W; Cushing, Johnathan B.

Research output: Contribution to journal › Article

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*, vol. 32, no. 7, pp. 1288-1301. https://doi.org/10.1364/JOSAA.32.001288

}

TY - JOUR

T1 - Shannon information and ROC analysis in imaging

AU - Clarkson, Eric W

AU - Cushing, Johnathan B.

PY - 2015

Y1 - 2015

N2 - Shannon information (SI) and the ideal-observer receiver operating characteristic (ROC) curve are two different methods for analyzing the performance of an imaging system for a binary classification task, such as the detection of a variable signal embedded within a random background. In this work we describe a new ROC curve, the Shannon information receiver operator curve (SIROC), that is derived from the SI expression for a binary classification task. We then show that the ideal-observer ROC curve and the SIROC have many properties in common, and are equivalent descriptions of the optimal performance of an observer on the task. This equivalence is described mathematically by an integral transform that maps the ideal-observer ROC curve onto the SIROC. This then leads to an integral transform relating the minimum probability of error, as a function of the odds against a signal, to the conditional entropy, as a function of the same variable. This last relation then gives us the complete mathematical equivalence between ideal-observer ROC analysis and SI analysis of the classification task for a given imaging system.We also find that there is a close relationship between the area under the ideal-observer ROC curve, which is often used as a figure of merit for imaging systems and the area under the SIROC. Finally, we show that the relationships between the two curves result in new inequalities relating SI to ROC quantities for the ideal observer.

AB - Shannon information (SI) and the ideal-observer receiver operating characteristic (ROC) curve are two different methods for analyzing the performance of an imaging system for a binary classification task, such as the detection of a variable signal embedded within a random background. In this work we describe a new ROC curve, the Shannon information receiver operator curve (SIROC), that is derived from the SI expression for a binary classification task. We then show that the ideal-observer ROC curve and the SIROC have many properties in common, and are equivalent descriptions of the optimal performance of an observer on the task. This equivalence is described mathematically by an integral transform that maps the ideal-observer ROC curve onto the SIROC. This then leads to an integral transform relating the minimum probability of error, as a function of the odds against a signal, to the conditional entropy, as a function of the same variable. This last relation then gives us the complete mathematical equivalence between ideal-observer ROC analysis and SI analysis of the classification task for a given imaging system.We also find that there is a close relationship between the area under the ideal-observer ROC curve, which is often used as a figure of merit for imaging systems and the area under the SIROC. Finally, we show that the relationships between the two curves result in new inequalities relating SI to ROC quantities for the ideal observer.

UR - http://www.scopus.com/inward/record.url?scp=84943250081&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943250081&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.32.001288

DO - 10.1364/JOSAA.32.001288

M3 - Article

C2 - 26367158

AN - SCOPUS:84943250081

VL - 32

SP - 1288

EP - 1301

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 - 7

ER -