Keystone
The left- and right-eye images of a point should be separated only horizontally. If there is a vertical difference between them, it is called vertical parallax. The vertical parallax that a converged rig produces in the corners of the frame is called keystone (keystone distortion).
Why it occurs
In a converged rig the two cameras are turned toward each other, so there is an angle of 2β between their image planes. A rectangular frame appears in the two images as two trapezoids tilted in opposite directions. At the center of the frame and along the horizontal and vertical center lines the vertical difference is negligible; it grows toward the corners (Woods, Docherty, Koch 1993). There is no closed-form formula for it; the calculator computes it by projecting each point into both cameras.
For the viewer
Vertical parallax carries no depth information. The eyes also try to adjust vertically to bring the two images into register; this leads to fatigue and, at large values, to double vision.
Magnitude
Keystone increases as the interaxial grows, as the convergence comes closer and as the lens gets wider. With a 150 mm interaxial and convergence at 2 m, the corner vertical parallax in a 1920-pixel image:
| Lens | Corner vertical parallax | 55" TV, 2.5 m (arcminutes) |
|---|---|---|
| 18 mm | 39 px | 34′ |
| 35 mm | 20 px | 17′ |
| 85 mm | 8 px | 7′ |
A commonly cited acceptance limit for vertical parallax is about 15 arcminutes (Terzić and Hansard). Woods et al. report that on a 16" monitor the vertical difference must be less than 7 mm for the two images to fuse.
Other sources of vertical parallax
Converged geometry is not the only source of vertical parallax. Small errors in rig alignment have the same effect:
- Height difference: one camera is higher than the other.
- Axis rotation: one camera is rotated around its optical axis (roll).
- Scale difference: the focal lengths or zoom positions of the two lenses are not equal.
- Lens difference: the two lenses differ in distortion or optical center.
Correction
In the geometric correction stage of mastering, vertical alignment, rotation, scale and keystone are corrected together. The keystone of a converged shot is removed by rotating each image back by β around its own center; see Converged rig. The calculator's result cards give the keystone to be corrected in mastering in pixels and arcminutes.