Computer Vision (20)

Even though a lot of people believe that a stereogram is exactly equivalent to seeing with both the eyes there is one major difference. Stereograms are generally shot by moving the camera horizontally by a short distance (in case of a single camera system) or by keeping two cameras side by side, which capture the horizontal disparity. Suppose there are two infinitely long horizontal bars, one at a certain distance from the other (both horizontally and vertically) and nothing else around it and you take a stereo image of this, with the camera taking the projection of their lengths, you will fail to capture the horizontal disparity, because there is none in this direction.

A camera takes the horizontal projection of objects (horizontal line pointing towards you), and so the distance between the horizontal bars along this direction cannot be shown in this 2D image. The vertical distance between them is ‘v’. In other words, if we try to capture this 3D setup in a stereo image pair to get the horizontal depth between the bars you will end up with exactly the same image in the left and right. There is no use seeing it stereoscopically, because, which point in the two images will the brain correspond? Since the camera is moved horizontally, the vertical distance between the two bars remains the same in the stereo image.

In a real scenario, how do our eyes and brain together manage to catch the right point? I mean, form a triangle and get the depth out of it. This is possible because, in addition to just 2D projection our eyes collect in real time one more parameter; focus. Focus is exactly the same as accommodation that I was describing in monocular cues. Our eye has to accommodate itself to focus (see sharply) objects at different depths. When object at one depth is seen sharply depending on the aperture of our eyes objects at other distance will be blur. This means that focus or accommodation is dependent on depth and unique for every distance from the eye. So the accommodation value would actually give the absolute depth of them object.

Computer Vision (19)

Disparity is a must to perceive depth in a stereoimage pair and so our brain needs at least two separated points with disparity to extract the distance between them. Disparity at a later stage would use triangulation to perceive depth, but this triangle would depend on the separation between the images and not the depth of the actual object. The below image illustrates triangulation from disparity when a stereogram is cross viewed.

The red lines are traced when the eyes combine the rectangle and the green lines when they combine the circle. The point of intersection of the red lines gives the 3D location of the rectangle and the green lines that of the circle. As mentioned earlier the circle is in front of the rectangle when cross viewed. One of the points for the formation of the triangle comes from the point of intersection of either the red or the green lines and the other two points are the two eyes. The distance of the point of intersection of lines from the two eyes (d), depends on the separation between the images, so the absolute distance of the objects remains unknown in the stereo image pair. The relative depth of different objects from one another is obtained by corresponding objects form the two images, which moves the point of intersection of the lines according to the 3D placement of the objects (similar to red and green lines).

This is not the case when we extract depth from the actual 3D surrounding because our eye makes use of triangulation from the convergence of the eyes and not disparity. Our eyes assist to perceive the absolute depth of our surrounding while in stereograms we can only perceive the relative depth of one object from the other.