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The relation between disparity and depth is derived based on the assumption that the two cameras are parallel.

Image rectification does not make this assumption valid.

But I see in many university computer vision lectures, with two rectified images, the depth map is directly calculated. I cannot figure out why.

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Image rectification does not make this assumption valid.

Yes it does!

From the wiki: https://en.wikipedia.org/wiki/Image_rectification

Image rectification warps both images such that they appear as if they have been taken with only a horizontal displacement and as a consequence all epipolar lines are horizontal.

The term can be used in an overloaded manner though, by instead implying that projective distortions from the camera are removed. So you have to be careful.

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