Computer Vision (14)

If you closely observe the first diagram in my earlier post, you will see a triangle formed whenever the two eyes see an object. The three lines that form it are; the line joining the left eye and the object it is currently seeing, the line joining the right eye and the object it is currently seeing and the line joining the two eyes. From the perspective of the eyes, they don’t know where the object is, because each of the eyes has only got a 2D projection of the surrounding including the object it is currently seeing. Assuming that there is a central system controlling the movement of the eyes, this is what it knows about them. The length of the line joining the two eyes is always a constant. In order to see an object it has to be placed on the macula of the retina and hence it knows the angle at which the eyes have converged. We can easily solve for the third point which is where the object is placed and hence we know its distance, which is the depth we are trying to perceive.

Knowing the distance between the eyes (D) and the angle of view of both the eyes (theta1 and theta2), we can always extend the two lines (shown dotted) to meet at a point (O). The perpendicular drawn from O to the line joining the eyes is the depth of the object from your eyes. Since the two eyes always see a common point, the lines emanating from them always converge and make sure that a triangle is formed for an object anywhere in the common 3D space.