Parallel vs. Toed-in Cameras

"There is a great deal of misunderstanding going on with Parallel vs. Converged topic. It is important to understand that there are actually three different categories of camera configuration (not just two):

(1) Parallel cameras WITHOUT image offset - In this model the lenses/cameras are parallel and the optical axes of the two cameras overlap at infinity. This model is usually what most people think of when the "Parallel" camera model is mentioned. Without any post shifting of the images to correct the zero parallax distance (ZPD), objects at infinity will be cast at the surface of the display and all other images will be cast in front of the display. Nothing appears behind the screen surface (no positive screen parallax).

(2) Parallel cameras WITH image offset - In this model the lenses/cameras are again parallel, however, the images are shifted either in post, or in the camera, by shifting the two imaging sensors (e.g. CCD) behind the lenses. This shifting of the images has the effect of changing the zero parallax distance (ZPD) (sometimes called the convergence distance). In this model, the ZPD is usually set mid way through the scene, meaning that some objects will appear behind the screen and some objects will appear in front of the screen.

(3) Toed-in cameras - In this model the cameras (and lenses) are rotated inwards so that their optical axes intersect at a point usually mid-way through the scene, so that some objects will appear behind the screen and some objects will appear in front of the screen. This is usually what most people think of when the "converged" camera model is mentioned. As has already been pointed out the "toed-in" camera model results in keystone distortion, but also "depth plane curvature" - flat planes can appear bowed in the centre toward the camera.

Note that I have not used the term "converged" to describe the last case. That is because it could be argued that both models (2) and (3) are converged. One definition of "converge" is "to come together". In the case of toed-in cameras, the optical axes of the two cameras obviously come together (usually to a point roughly midway in the scene). In the second camera model (parallel with image offset), if we consider the case where the image offset is generated by shifting the imaging sensor behind the lens, the optical axes of the two cameras are angled inwards (but not by rotation of the cameras/lenses). Where the optical axes intersect will be the zero parallax distance (assuming no further image offset in post). Since the two optical axes come together, the second model could also be called converged.

I am sure some will disagree with this interpretation, however I note that Lenny Lipton in a recent blog entry makes the same point as I am. Lenny's point is don't use the term "converged cameras" since it is so easily confused. My additional point would be don't just use the term "parallel cameras" since it is also so easily confused. If you do see the terms "parallel cameras" or "converged cameras" used, dig deeper to understand whether they mean camera model (1), (2) or (3).

It is important to point out that no-one in their right mind would use camera model (1) (Parallel WITHOUT image offset). As mentioned above, it would result in all images on a stereoscopic display being cast in front of the display and infinity objects would be shown on the surface of the 3D display. So really, when people talk about using the "Parallel camera model" they are probably really talking about using model (2) "Parallel cameras WITH image offset". In many ways it is equivalent to model (3) "toed-in cameras" but without the keystone distortion and depth-plane curvature. Model (2) is harder to achieve with real cameras than model (3) which is why people still tend to use model (3).

A few other important points:
- Convergence in itself does not create divergent 3D images (or divergent infinity). It is the poor selection of camera separation (interaxial) (i.e. too wide) when combined with close convergence, and large screen sizes, that produces divergent 3D images (divergent infinity).

- "Ghosts of the Abyss" by James Cameron provides some very good examples of what you should not do with stereoscopic cameras - e.g. pulling convergence. The biggest problem with the cameras used on this shoot was that the minimum interaxial separation of the stereoscopic cameras used was not suitable for the extreme closeups (and pulling convergence really close) that they did numerous times in this movie. The cameras were set side-by-side meaning that the minimum interaxial separation was quite large. I was pleased to read recently that Pace/Cameron now also have beam-splitter rigs - and therefore allowing more suitable camera separation, particularly for closeups.

- 3ality Digital used many 3D camera rigs to shoot U2-3D. Some were of their own design, but they didn't have enough and not enough time to make more, so they rented others in (including from Hineslab, and others). My understanding is that most of the stereoscopic camera rigs were of the beam-splitter design (which allows very narrow camera interaxial if required) rather than the side-by-side configuration.

- There are major differences in the ways that stereoscopic images can be captured in CG vs. CCD vs. film. Camera model (2) is very easy to achieve in CG, whereas it is difficult to achieve with CCDs which is why camera model (3) is often used. With film, there is no pixel accurate reference, so people are probably using camera model (2) while they think they are using camera model (1).

- If "keystone distortion" and "depth plane curvature" are still unclear to you, check out figures 8 and 7 respectively here. Note that this 1993 paper usually means "parallel cameras WITH image offset" when it refers to "parallel cameras" - which in turn could be contributing to the confusion."

By Andrew Woods