Linearity of each channel pixel values from a surface in and out of shadows and its applications

Shadows, the common phenomena in most outdoor scenes, are illuminated by diffuse skylight whereas shaded from direct sunlight. Generally shadows take place in sunny weather when the spectral power distributions (SPD) of sunlight, skylight, and daylight show strong regularity: they principally vary with sun angles. In this paper, we first deduce that the pixel values of a surface illuminated by skylight (in shadow region) and by daylight (in non-shadow region) have a linear relationship, and the linearity is independent of surface reflectance and holds in each color channel. We then use six simulated images that contain 1995 surfaces and two real captured images to test the linearity. The results validate the linearity. Based on the deduced linear relationship, we develop three shadow processing applications include intrinsic image deriving, shadow verification, and shadow removal. The results of the applications demonstrate that the linear relationship have practical values.