A projector-camera setup for geometry-invariant frequency demultiplexing

Consider a projector-camera setup where a sinusoidal pattern is projected onto the scene, and an image of the objects imprinted with the pattern is captured by the camera. In this configuration, the local frequency of the sinusoidal pattern as seen by the camera is a function of both the frequency of the projected sinusoid and the local geometry of objects in the scene. We observe that, by strategically placing the projector and the camera in canonical configuration and projecting sinusoidal patterns aligned with the epipolar lines, the frequency of the sinusoids seen in the image becomes invariant to the local object geometry. This property allows us to design systems composed of a camera and multiple projectors, which can be used to capture a single image of a scene illuminated by all projectors at the same time, and then demultiplex the frequencies generated by each individual projector separately. We show how imaging systems like those can be used to segment, from a single image, the shadows cast by each individual projector - an application that we call coded shadow photography. The method is useful to extend the applicability of techniques that rely on the analysis of shadows cast by multiple light sources placed at different positions, as the individual shadows captured at distinct instants of time now can be obtained from a single shot, enabling the processing of dynamic scenes.