Keystoning / Convergence Error

By Rick Wilson and John Bercovitz

Often someone new to 3D photography feels that, when taking a 3D pair, the camera should "toe-in" towards the subject. This misconception occurs in all 3D photography, but is most pronounced when taking a closeup (macro) shot. It is felt that the camera shots should point in, since that is what the human eye does. The following article describes the keystoning error which occurs if this is done.

What is keystoning (aka "convergence error")?

Consider what an ideal camera is supposed to do. Take an ideal distortion-free camera. Mark a grid of evenly spaced lines on a wall and point the camera at the grid covered wall. Make sure the camera's film plane is parallel to the wall. Take a picture. Look at the picture and it has a grid on it too. It is a "scale drawing" of the grid on the wall. You can lay a ruler on the picture and you will find all the lines are straight. You can use that ruler to measure all the squares in the grid and you'll find they're all the same size.

Now tilt the camera's film plane so it's no longer parallel to the grid-covered wall. Take another picture. This time the lines in the picture are still straight* but the squares are no longer all the same size. Also, the squares have become trapezoids or other sorts of quadrangles. These shapes are called "keystones".

If you take two pictures as shown in the illustration above, you will get keystoning. The left camera will make a picture with the small ends of the keystones on the right, while the right camera will have make a picture with the small ends of the keystones on the left, like this:

When you go to merge those two pictures in a viewer, you're going to have trouble. The flat wall becomes warped. If the keystoning is severe the pictures will be painful to view if they can be merged at all. As with a lot of these things, you can get tangled up. The first thing you're going to think is that the left illustration shows how your eyes see things. That's right. But remember your eyes are being presented with an evenly gridded wall in real life so they ought to be presented with the same thing in the viewer.

*I'm simplifying slightly here.

Rocky Mountain
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