Computer Vision (13)

By now, you all must have understood that to perceive 3D from 2D image(s), the image(s) need(s) to contain similar objects with disparity. How this disparity creates the sensation of depth in our brain is by triangulation, which I will be discussing now.

The vertical line in the below diagram is the bisector between the two eyes. The square, ellipse and circle are three different objects placed at different depths from the eyes. So, what you are viewing here is the top view of the objects along with your eyes. I have not shown the movement of the eye to see the different objects shown here just to keep the diagram simple. The objects are placed on the vertical line just to get a symmetric image on the sensor and to reduce the complexity of the drawings. The dotted lines give the field of view of each eye. To get a better understanding of whatever I am trying to explain here, I suggest the reader to try these out practically as and when he/she reads through it. This will make you understand the concepts very clearly.

The below diagram gives the 2D projection of the 3D environment shown above, that your eyes send to your brain. For the right eye the image of the square is always to its leftmost followed by the ellipse and the circle. For the left eye the image of the square is always to its rightmost followed by the ellipse and the circle. The left column in the image below is the image captured by the left eye (objects are marked with an ‘l’ on top), the right column is the image formed by the right eye (objects are marked with an ‘r’ on top) and the central column is the combined image formed in the brain (‘l’ is the image that has come from the left eye and ‘r’ is the image that has come from the right eye). ‘op’ in the diagram means the overlap point, the region where the two images are combined, which in our case is the macula. Let me explain it in 3 different cases:

1. When your eyes look at the square, the square is the region of overlap in the brain and therefore the square forms the center. Other objects are moved to the sides as named in the diagram. Imagine sliding the left and the right images close to each other such that the squares are placed one over the other.
2. When the eyes look at the ellipse, the ellipse forms the center, which is obtained by sliding the two images more towards each other so that the ellipse forms the center. Here the square from the right eye and the circle from the left eye and the circle from the right eye and the square from the left eye overlap each other. They are shown one above the other for the sake of clarity. How does our brain deal with the overlap of dissimilar objects? Will it average the two or suppress one of them? This is again binocular rivalry about which I will be posting later.
3. When the eyes see the circle, the circle forms the center, which is obtained by sliding the two images further towards each other to overlap on the circle.

Try these out practically and verify the results. Ooops! this post has grown so long, which I always try to avoid but…. Anyway I will come to triangulation in my next post once again