Regression Approach in the Evaluation of White’s Effect Magnitude in Comparison to Lightness

Abstract

In the achromatic White's grid, the grey patches between the grey lines are perceived as darker while the same elements inserted between white lines are perceived lighter than their true measured values. A number of authors attempted to calculate the magnitude and direction of this effect using mathematical models based on multiple spatial filters. This paper uses different mathematical model, based on regression analysis, which has shown itself as an excellent tool for prediction of direction and magnitude of White's effect. The psychophysical visual experiment was conducted on 38 subjects of both genders. The differences in lightness perception ∆L00 were calculated in CIE ∆E_2000 system. This paper determined the functional dependence of White's effect magnitude ∆L00 to the lightness L of rectangular elements in White's achromatic grid. The results gave the square polynomial of very high quality (R2 = 0,974). Regression polynomials were also found. The gave numerical values ∆L00 of difference in perception of left and right elements in comparison to their physical values (left R2 = 0,943, right R2 = 0,938) in dependence to variation of lightness parameter L. Results of the research clearly show the mathematical pattern of White's effect based on the lightness of rectangular elements.