in stereo matching is the disparity always to the left?

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Hello

I am trying to use stereo matching implementations of OpenCV. (StereoBM,StereoSGBM). But i am having some problems. The resulting disparity maps are always crop from one side.

OpenCV assumes that the disparity between a pair of rectified stereo image is always to left (is this correct?). I have some pairs where the disparity is both to the right and to the left. For the upper part of images, it is to the right then around middle it becomes almost zero and it switches towards left.

Therefore i have to assign a large disparity interval. This results in crop disparity images. Do you have any idea how to apply StereoBM or StereoSGBM for images like the ones i have?

Thanks