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### Notes:

So what is the problem of SC? We are given 2 images of the same real world scene, taken at the same time but from different cameras. We’ll call one of them the left image and the other the right image. Because the positions of the cameras are different, each real world point will project to pixels with different coordinates in each image. So here for example these 2 pixels are projections of the same physical point in the scene, the lamp corner. We will call such pixels corresponding, that is the pixels which correspond to the same physical scene element. Given left and right images, correspondences are unknown, of course. So the task of stereo correspondence is to determine the corresponding points. We will fix one image, say the left image, and for each point in the left image we will be looking for the point it corresponds to in the right image. Wlog we can assume that the y coordinates of the corresponding points are the same, only the x coordinates are different. So then to find a correspondence for a point in the left image, we only have to search along this line in the right image. The difference between the x coordinates of the corresponding points is called disparity. I will alternatevely say that given a pixel in the left image we are looking for the corresponding pixel in the right image, or that we are determining the disparity of that pixel in the left image. These 2 things are equivalent, if we know disparity, we know x2 and vice versa. Note that the disparity we compute is for the left image, and this image here shows the disparities for the left image.

From camera geometry it is easy to see that disparity is inversely proportional to depth. The larger the disparity is, the closer the object is to the cameras. Thus after correspondences are computed, we can determine the 3D scene structure from the computed disparities. Note that our eyes have the same set up. They use the disparity from the left eye image and the right eye image to figure out how far the object is. Disparity between the images is a major stereo cue and reason why we perceive the world in 3D. Human visual system has other cues than disparity for 3D world perception, however.