Characterizing the Shadow Space of Camera-Light Pairs

Abstract

We present a theoretical analysis for characterizing the shadows cast by a point light source given its relative position to the camera. In particular, we analyze the epipolar geometry of camera-light pairs, including unusual camera-light configurations such as light sources aligned with the camerapsilas optical axis as well as convenient arrangements such as lights placed in the camera plane. A mathematical characterization of the shadows is derived to determine the orientations and locations of depth discontinuities when projected onto the image plane that could potentially be associated with cast shadows. The resulting theory is applied to compute a lower bound on the number of lights needed to extract all depth discontinuities from a general scene using a multiflash camera. We also provide a characterization of which discontinuities are missed and which are correctly detected by the algorithm, and a foundation for choosing an optimal light placement. Experiments with depth edges computed using two-flash setups and a four-flash setup illustrate the theory, and an additional configuration with a flash at the camerapsilas center of projection is exploited as a solution for some degenerate cases.