Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds.

Models of human visual detection have been successfully used in computer-generated noise. For these backgrounds, which are generally statistically stationary, model performance can be readily calculated by computing the index of detectability d' from the noise power spectrum, the signal profile, and the model template. However, model observers are ultimately needed in more real backgrounds, which may be statistically non-stationary. We investigated different methods to calculate figures of merit for model observers in real backgrounds based on different assumptions about image stationarity. We computed performance of the nonpre-whitening matched-filter observer with an eye filter on mammography and coronary angiography for an additive or a multiplicative signal. Performance was measured either by applying the model template to the images or by computing closed-form expressions with various assumptions about image stationarity. Results show first that the structured backgrounds investigated cannot be considered stationary. Second, traditional closed-form expressions of detectability calculated from the noise power spectra with the assumption of background stationarity lead to erroneous estimates of model performance. Third, the most accurate way of measuring model performances is by directly applying the model template on the images or by computing a closed-form expression that does not assume image stationarity.