The search-model
In the search-model parameterization the clustered fixations, termed decision sites, are the suspicious regions that were flagged for further examination. Decision sites corresponding to normal regions are termed noise sites and those corresponding to lesions are termed signal sites. The numbers of noise and signal sites are modeled as random integers sampled from Poisson and binomial distributions, respectively. Corresponding to the cognitive analysis stage, at each decision site the observer computes a decision variable or z-sample. The model assumes that z-samples for noise and signal sites are sampled from normal distributions separated by a signal-to-noise ratio parameter. If a z-sample exceeds the observer's lowest reporting threshold the the corresponding region is marked (or reported). The rating assigned to a mark is the value of the z-sample..
The search-model for a single rating study is illustrated below for a hypothetical image with 6 noise sites (dotted up arrows) and 3 signal sites (solid up arrows). The normal distributions labeled "noise" and "signal" determine the z-samples for noise and signal-sites, respectively. Two noise site z-samples exceed the cutoff zeta, leading to 2 non-lesion localizations ("false positives") and 2 signal site z-samples exceed the cutoff, leading to 2 lesion localizations ("true positives") for a total of 4 marks on this image. Assuming the image has 5 lesions the estimates of Poisson and binomial parameters - based on this one image sample - are 6 and 0.6, respectively. Averaging these over a large number of images yields the true values of these parameters. For details see these references.
