The two ellipses are the two eyes. A, B, C and D are 4 objects such that B and C are identical. Objects A and D are exactly along the line bisecting the horizontal line joining the two eyes. B and C are placed such that the images projected by them in the two eyes occupy the same place as that occupied by A. B is not seen by the left eye and C is not seen by the right eye, because D projects itself in the same space as B and C in the left and right eyes respectively. Let’s now consider two cases.

Case1: Suppose only D and A are present in the diagram, the right eye has the image of D to the left of A and the left eye has the image of D to the right of A. You get a certain disparity map for this arrangement and that would indicate the correct depth between the objects A and D.

Case2: Now suppose B and C are introduced in the diagram, A is no longer visible. In fact the two new objects are projecting themselves in the same place as that of A and therefore since the objects are identical it would produce the same disparity map as earlier. But now the disparity map has failed to produce the right result.

This means that there should be a new way to look at the problem itself! Trying to solve it after the image formation is of no use as we have no extra information to distinguish between the objects A and either B or C. Since this problem is an old one and well known among computer vision scientists, a lot of attempts were made to solve the problem by making use of the focus parameter i.e. depth from focus. If you know where one of your cameras is focused and the angle that its optical axis makes with the horizontal, then you could readily pin point the location of the point along the plane of the eye. With this information being passed on to the other eye even this eye could know where it is supposed to see. Then a matching can be done and the objects at a particular depth can be easily segmented. This method definitely eliminates the search for a stereo match, but in reality there isn’t a perfect focusing method. So you definitely do not know whether the information you are passing is right or wrong. Even if you find an accurate focusing technique, such as the one that I have described in the article on focus, what if your robot mistakenly wears spectacles? Even though the object is correctly focused, the focus value obtained now is different from the one that will be obtained with out the spectacle. You are again passing the wrong information to the other camera!

Here is a new method using the results of the double slit experiment. The two eyes are considered as the two slits of the experiment and the source of light is the point that is to be matched by the two eyes. This method is independent of whether the eye has focused or not and hence independent of the focusing technique used. I am not a physicist and therefore cannot describe this technique in full detail from the physics point of view, but can somehow manage to scan the entire process to give you a good idea.

In a two slit experiment the source of light is a LASER and it is a single source. In order to get these two into the vision scenario let me assume that, the eye is capable of allowing only that photon that enters it along the optical axis to participate in the game called interference. This holds good only for one eye, say in this case it is the left eye. One of the eyes has to take predominance over the other so that this happens. This is because you always view an object or a point that lies on the optical axis of the two eyes, or in case of binocular rivalry it will be one eye. This would happen after the stereo correspondence is over, initially only one eye will be in the right direction. Now the problem is to get the right eye to the an angle at which it would be able to correspond the two points exactly. At any point on the surface of the lens or eye we can say that the photons can come from any direction. For the right eye we will consider only those photons that arrive at the center of the lens (the first point on the lens that the optical axis meets), and in any direction. Let us assume that it is capable of sampling the photons in any direction at any time. The technology to achieve these things may not be present at the time of writing this document, but let’s just try putting it in theory. So the right eye is going to sample each direction and allow the photons coming in that particular direction to participate in the game. The interference pattern produced will be from the photons that are arriving from the two eyes similar to the two slits. We still need to embed the aspect of LASER into this? For this to happen we have to give some more super powers to our lens. Let us assume that at the point of entry, the photons are down converted to a particular single frequency or filtered. So each eye is going to allow only one particular frequency, while the frequency selected may be different in both the eyes. Since the frequencies in both the eyes are known, the interference pattern can be interpreted without any problems. Instead of confusing ourselves a lot let us assume that there are a common set of visible frequencies between the eyes, and if it is not there let’s skip that direction. Here the only aim is to get an idea of how the double slit experiment will be used to solve the stereo correspondence problem and so I will make it as simple as possible with more than required assumptions at times. Every direction is going to give one or the other pattern, and our problem is to select the right one.

        For one particular common frequency we have an interference pattern, and with the help of it we guess the location of the point on the plane of the eye. If the photons in the two eyes are not coming from a single point, this will be a wrong guess. So we go on to verify it with a next common frequency. If the guessed point were right we already know the pattern that should appear. If the expected pattern matches with the pattern that is formed now the guessed point should be right! The right eye need not sample or scan the directions 3 dimensionally, because the plane of the eyes is already known. It only traces a semicircle to find a perfect match.