The average of the log-luminance of a large number of photographs from the same camera model with the same lens setting has a particular structure: the average images have a vertical gradient, but no horizontal gradient. This is the prior that we use to estimate vignetting for lens settings of specific camera models.

(a) Average log-luminance of 15,550 photographs captured by Canon S1IS cameras with focal length 5.8 mm and f-number 4.5. The photographs, all 2048x1536, were linearized and vignette corrected before averaging. (b) Average log-luminance of 13,874 photographs captured by Canon S1IS cameras with focal length 5.8 mm and f-number 2.8. (c,d) Contrast-enhanced versions (for illustration only) of the images in (a) and (b), respectively. (e,f) Plots of the average log-luminances of respectively the 1000th column and 1000th row for the two settings in (a) and (b). Response functions were normalized so that luminance values were in the range (0,255) prior to averaging.