Computer Vision (18)

Disparity is something that is required to perceive depth from 2D stereo image pairs. For example, to create a stereo image pair in a computer as shown below, I just placed a rectangle and a circle one beside the other in the left image, copied the same thing for the right image as well, and then increased the distance between the rectangle and the circle in the right image.

The 3D interpretation of it is as follows. The image seen below is the top view of the 3D space whose 2D projection is shown above. On cross viewing it, you would see the circle in front of the rectangle. Cross viewing a stereogram means, your left eye would see the image on the right and your right eye the one on the left.

The dotted lines are the angle of view of the eyes (not to scale). The blue lines are the projection lines of the objects on the respective eyes. Since the eyes are placed at some distance from one another the projection of the objects in 3D space will always be different on both the eyes, except when the objects are on the vertical bisector. This difference in the projection lengths is what disparity is.

Disparity = length of the red line - length of the green line.

From the diagram it is clearly evident why the distance between the rectangle and the circle in the right image (red line) is kept greater than the left image (green line) to recreate this 3D effect in the brain when viewed stereoscopically. Think about how the gap should be to view the circle behind the rectangle.