International Journal of Computer Vision manuscript No. (will be inserted by the editor) Radial Multi-focal Tensors Applications to Omnidirectional Camera Calibration (original) (raw)

The 1D radial camera maps all points on a plane, containing the principal axis, onto the radial line which is the intersection of that plane and the image plane. It is a sufficiently general model to express both central and non-central cameras, since the only assumption it makes is of known center of distortion. In this paper, we study the multi-focal tensors arising out of 1D radial cameras. There exist no two-view constraints (like the fundamental matrix) for 1D radial cameras. However, the 3-view and 4-view cases are interesting. For the 4-view case we have the radial quadrifocal tensor, which has 15 d.o.f and 2 internal constraints. For the 3-view case, we have the radial trifocal tensor, which has 7 d.o.f and no internal constraints. Under the assumption of a purely rotating central camera, this can be used to do a non-parametric estimation of the radial distortion of a 1D camera. Even in the case of a non-rotating camera it can be used to do parametric estimation, assuming a ...