Radial Multi-focal Tensors

摘要

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 planar scene. Finally we examine the mixed trifocal tensor, which models the case of two 1D radial cameras and one standard pin-hole camera. Of the above radial multifocal tensors, only the radial trifocal tensor is useful practically, since it doesn’t require any knowledge of the scene and is extremely robust. We demonstrate results based on real-images for this.