Fundamentals of the Human Foveal Vision System

Abstract : This paper presents a mathematical model, which includes a closed-form equation (the ABCt law) that generates the entire Blackwell-McCready (BM) threshold data set. It derives relationships among the four fundamental parameters of foveal vision: target area A, background luminance B, threshold contrast C and stimulus presentation time t. It shows that graphs of log (t) as a function of log (ABC) are hyperbolas whose asymptotic regions are related to the well known laws of Weber- Fechner and Bloch. It unifies important relationships associated with target/background scene parameters as they relate to the human foveal vision process. The constants associated with the simple empirical laws of Ricco, Blackwell, Weber-Fechner and Bloch can easily be obtained for a large range of target `background conditions and stimulus presentation times. Conditions for the most efficient stimulation of the human visual system are quantified and expressed in terms of the total energy for specific detection tasks.