Abstract
This paper presents a simple mathematical performance model of the human foveal vision system based on an extensive analysis of the Blackwell-McCready (BM) data set. It includes a closed-form equation, the (ABC)t law, that allows the analyst to predict the entire range of BM threshold data. Relationships are derived among the four fundamental parameters of foveal vision: target area A, background luminance B, threshold contrast C, and stimulus presentation time t. Hyperbolic-curve fits on log-log plots of the data lead to the well-known laws of Ricco, Blackwell, Weber and Fechner, and Bloch. This paper unifies important relationships associated with target and background scene parameters as they relate to the human foveal vision process. The process of detecting a BM target, using foveal vision, is reduced to the total temporal summation of light energy modified by a multiplicative energy ratio. A stochastic model of human observer performance is presented in terms of a cumulative Gaussian distribution, which is a function of the apparent and BM contrast threshold values.
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