Diffuse Mirrors: 3D Reconstruction from Diffuse Indirect Illumination Using Inexpensive Time-of-Flight Sensors

The functional difference between a diffuse wall and a mirror is well understood: one scatters back into all directions, and the other one preserves the directionality of reflected light. The temporal structure of the light, however, is left intact by both: assuming simple surface reflection, photons that arrive first are reflected first. In this paper, we exploit this insight to recover objects outside the line of sight from second-order diffuse reflections, effectively turning walls into mirrors. We formulate the reconstruction task as a linear inverse problem on the transient response of a scene, which we acquire using an affordable setup consisting of a modulated light source and a time-of-flight image sensor. By exploiting sparsity in the reconstruction domain, we achieve resolutions in the order of a few centimeters for object shape (depth and laterally) and albedo. Our method is robust to ambient light and works for large room-sized scenes. It is drastically faster and less expensive than previous approaches using femtosecond lasers and streak cameras, and does not require any moving parts.