A Closed Form Solution for the Self-Calibration of Heterogeneous Sensors

We present a novel closed-form solution for the joint self-calibration of video and range sensors. The approach single assumption is the availability of synchronous time of flight (i.e., range distances) measurements and visual position of the target on images acquired by a set of cameras. In such case, we make explicit a rank constraint that is valid for both image and range data. This rank property is used to find an initial and affine solution via bilinear factorization, which is then corrected by enforcing the metric constraints characteristic for both sensor modalities (i.e., camera and anchors constraints). The output of the algorithm is the identification of the target/range sensor position and the calibration of the cameras. The application extent of our approach is broad and versatile. In fact, with the same framework, we can deal with, but not restricted to, two very different applications. The first is aimed at calibrating cameras and microphones deployed in an unknown environment. The second uses a RGB-D device to reconstruct the 3D position of a set of keypoints using the camera and depth map images. Synthetic and real tests show the algorithm performance under different levels of noise and configurations of target locations, number of sensors and cameras.