The above mathematical formalism is limited in that it does not account for human visual system response to edge sharpness between adjacent scenic features or to changes in contiguous contrast for features with varying size. More modern psycho-
physical perception threshold formalisms can be constructed to incorporate the eye-brain system response to variations in edge sharpness between landscape features as well as variation in spatial frequency of landscape scenic elements (Carlson and Cohen, 1978; Campbell and Robson, 1964; Campbell et al., 1968; Campbell and Kulikowski, 1986; Henry, 1977; Malm, 1985; Malm et al., 1987). Any approach that incorporates the human response to spatial frequencies (size and shape effects) is most easily handled using linear system theory. A first step is to develop a quantitative descriptor of the scene itself.
A scene can be decomposed into light and dark bars of various spatial frequencies and intensities whose brightness change is proportional to a sine wave function. Equivalent contrast, Ceq, is just the average contrast of those sine waves within specified frequencies. Therefore, equivalent contrast can be calculated either for all spatial frequencies or only for those frequencies to which the human visual system responds. Then Ceq can be used in human visual system models to estimate the probability that a human observer will notice a change in the appearance of a landscape feature as aerosols are added or removed from the atmosphere.
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