Single-pixel three-dimensional dual photography

We report single-pixel three-dimensional (3D) dual photography. Inspired by a tri-linkage between single-pixel imaging, fringe projection profilometry (FPP), and dual photography, we propose a method for 3D imaging that allows for the synthesis of dual and relit images in a camera-free context. By using FPP calibration methods and implementing a direct coordinate mapping with phase shifting, we obtain highly efficient measurements of the direct component of the scene light transport matrix, while simultaneously sensing the surface profiles of 3D objects. Through the addition of calibration information and by exploiting Helmholtz reciprocity, dual photography and scene relighting can thus be performed on 3D images. To verify the proposed imaging method, we have developed a light-path symmetric single-pixel imaging system based on two digital micromirror devices (DMDs). As a benefit of this choice of imaging platform, the traditionally distinct roles of projector and camera hardware can be freely interchanged, depending only on the DMD hardware chosen for the deployment of modulation patterns. For the acquisition of images, binary cyclic S-matrix patterns and binary sinusoidal fringe patterns are loaded onto each DMD for scene encoding and virtual fringe projection, respectively. Using this system, we further demonstrate the broadening of traditional dual photography image synthesis to viewing and relighting of 3D images at user-selectable perspectives. Our work extends the conceptual scope and the imaging capability of dual photography.