Effect of random background inhomogeneity on observer detection performance.

Many psychophysical studies of the ability of the human observer to detect a signal superimposed upon a uniform background, where both the signal and the background are known exactly, have been reported in the literature. In such cases, the ideal or the Bayesian observer is often used as a mathematical model of human performance since it can be readily calculated and is a good predictor of human performance for the task at hand. If, however, the background is spatially inhomogeneous (lumpy), the ideal observer becomes nonlinear, and its performance becomes difficult to evaluate. Since inhomogeneous backgrounds are commonly encountered in many practical applications, we have investigated the effects of background inhomogeneities on human performance. The task was detection of a two-dimensional Gaussian signal superimposed upon an inhomogeneous background and imaged through a pinhole imaging system. Poisson noise corresponding to a certain exposure time and aperture size was added to the detected image. A six-point rating scale technique was used to measure human performance as a function of the strength of the nonuniformities (lumpiness) in the background, the amount of blur of the imaging system, and the amount of Poisson noise in the image. The results of this study were compared with earlier theoretical predictions by Myers et al. [J. Opt. Soc. Am. A 7, 1279 (1990)] for two observer models: the optimum linear discriminant, also known as the Hotelling observer, and a nonprewhitening matched filter. Although the efficiency of the human observer relative to the Hotelling observer was only approximately 10%, the variation in human performance with respect to varying aperture size and exposure time was well predicted by the Hotelling model. The nonprewhitening model, on the other hand, fails to predict human performance in lumpy backgrounds in this study. In particular, this model predicts that performance will saturate with increasing exposure time and drop precipitously with increasing lumpiness; neither effect is observed with human observers.