In this paper, we present a theory for combining the effects of motion, illumination, 3D structure, albedo, and camera parameters in a sequence of images obtained by a perspective camera. We show that the set of all Lambertian reflectance functions of a moving object, at any position, illuminated by arbitrarily distant light sources, lies "close" to a bilinear subspace consisting of nine illumination variables and six motion variables. This result implies that, given an arbitrary video sequence, it is possible to recover the 3D structure, motion, and illumination conditions simultaneously using the bilinear subspace formulation. The derivation builds upon existing work on linear subspace representations of reflectance by generalizing it to moving objects. Lighting can change slowly or suddenly, locally or globally, and can originate from a combination of point and extended sources. We experimentally compare the results of our theory with ground truth data and also provide results on real data by using video sequences of a 3D face and the entire human body with various combinations of motion and illumination directions. We also show results of our theory in estimating 3D motion and illumination model parameters from a video sequence
['Yilei Xu', 'Amit K. Roy-Chowdhury']
Integrating Motion, Illumination, and Structure in Video Sequences with Applications in Illumination-Invariant Tracking