What can we learn about the scene structure from three orthogonal vanishing points in images

The problem of 3D Euclidean reconstruction of structured scenes from uncalibrated images based on the property of vanishing points is studied in this paper. Under the assumption of three-parameter-camera model with varying parameters, we prove that under an arbitrary preassigned world coordinate system, the camera projection matrix of an image can be uniquely determined from three mutually orthogonal vanishing points obtained from the image. When multiple images of the object are present, it is proved that the global consistent projection matrices can be recovered if an arbitrary reference point in space is observed across the views. For the scenario with multiple objects, we may reconstruct each object individually by the proposed method, then register and align them together via the technique of visual metrology so as to obtain the 3D structure of the entire scene. Compared with previous stereovision techniques, the proposed method avoids the bottleneck problem of feature matching and is easy to implement, therefore, more accurate, robust and realistic results are expected. Extensive experiments on synthetic and real world images validate the effectiveness of the proposed method.