Estimation of the orientation and distance of a mirror from Kinect depth data

In many common applications of Microsoft Kinect™ including navigation, surveillance, 3D reconstruction, and the like; it is required to estimate the geometry of mirrors or other reflecting surfaces existing in the field of view. This often is difficult as in most positions a mirror does not support diffuse reflection of speckles and hence cannot be seen in the Kinect depth map. A mirror shows up as unknown depth. However, suitably placed objects reflecting in the mirror can provide important clues for the orientation and distance of the mirror. In this paper we present a method using a ball and its mirror image to set-up point-to-point correspondence between object and image points to solve for the geometry of the mirror. With this simple estimators are designed for the orientation and distance of a plane vertical mirror with respect to the Kinect camera. In addition an estimator is presented for the diameter of the ball. The estimators are validated through a set of experiments.