Grayscale−luminance converting polynomial function for digital images to determine Feu and Lav in a low-contrast artificial lit space

The evaluation of the spatial luminance coefficient, Feu, and average luminance, Lav, can improve the lighting quality from both subjective and objective aspects. In the design survey, the determination of these indicators relies on the manual sampling of the luminance of measurement points, which is time-consuming and labour-intensive. This article proposes a grayscale−luminance converting polynomial function, and a method for the determination of Feu and Lav from digital images via the function. The acceptability index, Nallow, is created as the key parameter of the polynomial function, which reduces the number of required measurement points to 9. Taking visual comfort as the criterion, three types of low-contrast working conditions with different luminance distributions – namely an actual scene, simulated scenes and experimental scenes – were set, the luminance ratios of which were less than 100 and the luminance of which was less than 1000 cd/m2. To minimise the error to within 10%, the piecewise function of Nallow determined by the luminance ratio was constructed, which is obtained via the data verification and correction of 20 working conditions. The experimental results of a test scene demonstrate that the accuracies of Feu and Lav produced by the proposed polynomial function were better than those produced by an exponential function.