On the dimensionality of video bricks under varying illumination

Illumination models of the image set of an object (e.g., human face) under varying lighting conditions have been either empirically or analytically explored. However, the theoretical dimensionality of video bricks of an object under varying illumination is still unknown. In this paper, we focus on this question concretely and give both analytical and empirical results. We derive the theoretical upper bound of the dimensionality of video bricks by investigating the analytical formula of appearance changes due to motion variables of light sources. Theoretical results show in real-world scenes video bricks of an object under varying illumination could be expressed well by a low-dimensional linear subspace. Empirical results of the principal component analysis on the YaleB Face database and our video database are consistent with the theoretical results completely. The application of the low-dimensional linear models of video bricks is demonstrated by the foreground detection task in visual surveillance with drastic illumination changes.