Relighting with the reflected irradiance field: representation, sampling and reconstruction

Image-based relighting (IBL) is a technique to change the illumination of an image-based object/scene. In this paper, we define a representation called the reflected irradiance field which records the reflection from an object surface irradiated by a point light source that moves on a plane. This representation is dual to that of the light field. It synthesizes a novel image under a different illumination by interpolating and superimposing appropriate recorded samples. Furthermore, we study the minimum sampling problem of the reflected irradiance field, i.e., how many point light sources are needed during sampling. We find that there exists a geometry-independent bound for the sampling interval whenever the second-order derivatives of the surface BRDF and the minimum depth of the scene are bounded. This bound ensures that the error in the reconstructed image is controlled by a given tolerance, regardless of the geometry. Experiments on both synthetic and real surfaces are conducted to verify our analysis.