### Abstract

In localization tasks, an observer is asked to give the location of some target or feature of interest in an image. Scanning linear observer models incorporate the search implicit in this task through convolution of an observer template with the image being evaluated. Such models are becoming increasingly popular as predictors of human performance for validating medical imaging methodology. In addition to convolution, scanning models may utilize internal noise components to model inconsistencies in human observer responses. In this work, we build a probabilistic mathematical model of this process and show how it can, in principle, be used to obtain estimates of the observer template using maximum likelihood methods. The main difficulty of this approach is that a closed form probability distribution for a maximal location response is not generally available in the presence of internal noise. However, for a given image we can generate an empirical distribution of maximal locations using Monte-Carlo sampling. We show that this probability is well approximated by applying an exponential function to the scanning template output. We also evaluate log-likelihood functions on the basis of this approximate distribution. Using 1,000 trials of simulated data as a validation test set, we find that a plot of the approximate log-likelihood function along a single parameter related to the template profile achieves its maximum value near the true value used in the simulation. This finding holds regardless of whether the trials are correctly localized or not. In a second validation study evaluating a parameter related to the relative magnitude of internal noise, only the incorrect localization images produces a maximum in the approximate log-likelihood function that is near the true value of the parameter.

Original language | English (US) |
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Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Publisher | SPIE |

Volume | 9416 |

ISBN (Print) | 9781628415063 |

DOIs | |

State | Published - 2015 |

Event | Medical Imaging 2015: Image Perception, Observer Performance, and Technology Assessment - Orlando, United States Duration: Feb 25 2015 → Feb 26 2015 |

### Other

Other | Medical Imaging 2015: Image Perception, Observer Performance, and Technology Assessment |
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Country | United States |

City | Orlando |

Period | 2/25/15 → 2/26/15 |

### Fingerprint

### Keywords

- and observer modeling
- localization task
- ramp-spectrum noise
- Scanning linear template
- search models

### ASJC Scopus subject areas

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

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(Vol. 9416). [94160O] SPIE. https://doi.org/10.1117/12.2082874

**Approximate maximum likelihood estimation of scanning observer templates.** / Abbey, Craig K.; Samuelson, Frank W.; Wunderlich, Adam; Popescu, Lucretiu M.; Eckstein, Miguel P.; Boone, John M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*vol. 9416, 94160O, SPIE, Medical Imaging 2015: Image Perception, Observer Performance, and Technology Assessment, Orlando, United States, 2/25/15. https://doi.org/10.1117/12.2082874

}

TY - GEN

T1 - Approximate maximum likelihood estimation of scanning observer templates

AU - Abbey, Craig K.

AU - Samuelson, Frank W.

AU - Wunderlich, Adam

AU - Popescu, Lucretiu M.

AU - Eckstein, Miguel P.

AU - Boone, John M

PY - 2015

Y1 - 2015

N2 - In localization tasks, an observer is asked to give the location of some target or feature of interest in an image. Scanning linear observer models incorporate the search implicit in this task through convolution of an observer template with the image being evaluated. Such models are becoming increasingly popular as predictors of human performance for validating medical imaging methodology. In addition to convolution, scanning models may utilize internal noise components to model inconsistencies in human observer responses. In this work, we build a probabilistic mathematical model of this process and show how it can, in principle, be used to obtain estimates of the observer template using maximum likelihood methods. The main difficulty of this approach is that a closed form probability distribution for a maximal location response is not generally available in the presence of internal noise. However, for a given image we can generate an empirical distribution of maximal locations using Monte-Carlo sampling. We show that this probability is well approximated by applying an exponential function to the scanning template output. We also evaluate log-likelihood functions on the basis of this approximate distribution. Using 1,000 trials of simulated data as a validation test set, we find that a plot of the approximate log-likelihood function along a single parameter related to the template profile achieves its maximum value near the true value used in the simulation. This finding holds regardless of whether the trials are correctly localized or not. In a second validation study evaluating a parameter related to the relative magnitude of internal noise, only the incorrect localization images produces a maximum in the approximate log-likelihood function that is near the true value of the parameter.

AB - In localization tasks, an observer is asked to give the location of some target or feature of interest in an image. Scanning linear observer models incorporate the search implicit in this task through convolution of an observer template with the image being evaluated. Such models are becoming increasingly popular as predictors of human performance for validating medical imaging methodology. In addition to convolution, scanning models may utilize internal noise components to model inconsistencies in human observer responses. In this work, we build a probabilistic mathematical model of this process and show how it can, in principle, be used to obtain estimates of the observer template using maximum likelihood methods. The main difficulty of this approach is that a closed form probability distribution for a maximal location response is not generally available in the presence of internal noise. However, for a given image we can generate an empirical distribution of maximal locations using Monte-Carlo sampling. We show that this probability is well approximated by applying an exponential function to the scanning template output. We also evaluate log-likelihood functions on the basis of this approximate distribution. Using 1,000 trials of simulated data as a validation test set, we find that a plot of the approximate log-likelihood function along a single parameter related to the template profile achieves its maximum value near the true value used in the simulation. This finding holds regardless of whether the trials are correctly localized or not. In a second validation study evaluating a parameter related to the relative magnitude of internal noise, only the incorrect localization images produces a maximum in the approximate log-likelihood function that is near the true value of the parameter.

KW - and observer modeling

KW - localization task

KW - ramp-spectrum noise

KW - Scanning linear template

KW - search models

UR - http://www.scopus.com/inward/record.url?scp=84932172216&partnerID=8YFLogxK

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U2 - 10.1117/12.2082874

DO - 10.1117/12.2082874

M3 - Conference contribution

AN - SCOPUS:84932172216

SN - 9781628415063

VL - 9416

BT - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

PB - SPIE

ER -