When I say a surface is plain it has no contrast. If our brain used contrast to focus on a subject, would it fail to see a plain image? Curiously thinking of an answer to this I started reading some recent(2005) papers on what were the proposals to do so. First of all let me ask you, do you really see the slant for plain surfaces? Keep an answer in your mind and I will come back to it at the end.

    First let me discuss about the paper. It is obvious that when we see a slant surface the 2d images of the slant object will be of different sizes in both the eyes. So now, you don't have a pixel-wise correspondence. Each pixel of one eye is linked to a scalar multiple number of pixels in the other. Remember this statement, I will come back to this again. So what the paper does is to match not the pixels but correspond the image linewise. Suppose you are looking at a slant rectangle, the width of the rectangle in one eye is matched with the other. Using some simple math you can determine its slantness, hence your camera perceives depth, slant depth! Only because the rectangles are of different sizes in both the images, you cannot straight away conclude that the surface is slant. Difference in lengths can also be due to occlusions. So how does this paper take a decision between the two? If the surface is slant, to the left and right sides of it you will find single images which do not have correspondence, while if the slant surface is occluded by some other object, the occluding object will be seen by both the eyes.

    Let me express what I feel about this algorithm. Suppose I have a slant surface, do my eyes always register different widths? Let me take a slant surface, place it at the center of my visual field and put a rectangular window between me and the slant surface. Make sure that the slant surface you have taken for this experiment is really a plain one! The assumption made in the paper is now gone, since both the eyes now register the same width due to the presence of the window. So a camera equipped with such an algorithm would fail to perceive the slant.

    One interesting thing to be noted here is that not only does the algorithm fail in such a case, but also our eye, shocking! It is true, try it yourself.

 

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    The figure above is a stereo image. With cross eye one should see a closer left plane and a farther right plane, behind a black background. With parallel eyes one would see the right white plane closer than the left white plane. So when viewed stereoscopically you will be able to see depth between the planes. The black color just stays as a void background without any defined depth.

    Now let me interconnect the two planes by another rectangular plane (gray). Try to see the above picture in one of the stereoscopic ways described earlier. If you still don't know to see 3D follow this link

    Do the two planes apper at different depths? Atleast I don't see it!, mail me if you can. Our eye cannot see 3D because it cannot perceive the different sized gray rectangles as slant depth. Let me confuse you now.

    When you view this image stereoscopically, you will see a rectangle partially rotating back and forth. If our eye cannot perceive slant depth from two different sized rectangles, how is it able to see the rotation here? So am I wrong?

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