It´s All Done with Mirrors: Calibration-and-Correspondence-Free 3D Reconstruction

We describe a 3-D object reconstruction method using a stationary camera and a planar mirror. No external calibration is required. The mirror provides the extra views needed for a multiple-view reconstruction. We examine the imaging geometry of the camera-mirror setup and prove a theorem that gives us the constraints for computing the orientation of the mirror. The constraints are derived from the convex hull of the silhouettes of the images of the object and its mirror reflection. The distance between the mirror and the camera can be then obtained by a single object point or a pair of points on the mirror. After the pose of the mirror is determined, we have multiple calibrated views of the object. We present are construction method customized for the special imaging geometry.