Extended Multiple View Geometry for Lights and Cameras from Photometric and Geometric Constraints

In this paper, we derive a novel multilinear relationship for close light sources and cameras. In this multilinear relationship, image intensities and image point coordinates can be handled in a single framework. We first derive a linear representation of image intensity taken under a general close light source. We next analyze multiple view geometry among close light sources and cameras, and derive novel multilinear constraints among image intensity and image coordinates. In particular, we study the detail of the multilinear relationship among 7 lights and a camera. Finally, we show some experimental results, and show that the new multilinear relationship can be used for linearly generating images illuminated by arbitrary close light sources.