A Combined Theory of Defocused Illumination and Global Light Transport

Projectors are increasingly being used as light-sources in computer vision applications. In several applications, they are modeled as point light sources, thus ignoring the effects of illumination defocus. In addition, most active vision techniques assume that a scene point is illuminated only directly by the light source, thus ignoring global light transport effects. Since both defocus and global illumination co-occur in virtually all scenes illuminated by projectors, ignoring them can result in strong, systematic biases in the recovered scene properties. To make computer vision techniques work for general real world scenes, it is thus important to account for both these effects.In this paper, we study the interplay between defocused illumination and global light transport. We show that both these seemingly disparate effects can be expressed as low pass filters on the incident illumination. Using this observation, we derive an invariant between the two effects, which can be used to separate the two. This is directly useful in scenarios where limited depth-of-field devices (such as projectors) are used to illuminate scenes with global light transport and significant depth variations. We show applications in two scenarios: (a) accurate depth recovery in the presence of global light transport, and (b) factoring out the effects of illumination defocus for correct direct-global component separation. We demonstrate our approach using scenes with complex shapes, reflectance properties, textures and translucencies.