Resampling radially captured images for perspectively correct stereoscopic display

When rendering or capturing stereoscopic images, two arrangements of the cameras are possible: radial (“toed-in”) and parallel. In the radial case all of the cameras’ axes pass through a common point; in the parallel case these axes are parallel to one another. The radial configuration causes distortions in the viewed stereoscopic image, manifest as vertical misalignments between parts of the images seen by the viewer’s two eyes. The parallel case does not suffer from this distortion, and is thus considered to be the more correct method of capturing stereoscopic imagery. The radial case is, however, simpler to implement than the parallel: standard cameras or renderers can be used with no modification. In the parallel case special lens arrangements or modified rendering software is required. If a pinhole camera is assumed it should be readily apparent that the same light rays pass through the pinhole in the same directions whether the camera is aligned radially to or parallel to the other cameras. The difference lies in how these light rays are sampled to produce an image. In the case of a non-pinhole (real) camera, objects in focus should behave as for the pinhole case, while objects out of focus may behave slightly differently. The geometry of both radial and parallel cases is described and it is shown how a geometrical transform of an image produced in one case can be used to generate the image which would have been produced in the other case. This geometric transform is achieved by a resampling operation and various resampling algorithms are discussed. The resampling process can result in a degradation in the quality of the image. An indication of the type and severity of this degradation is given.