Doubt with disparity values from stereo image

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@LBerger: From your post, it seems you have mentioned the disparity value (depth info) is obtained is basically displacement from optical center till the object in view. Is my understanding correct? Basically I need the disparity in terms of perpendicular distance with plane of camera rather than center of camera. So I am using a pixel's cosine of cast angle with the camera's optical axis (obtained using FOV parameters of camera). Is this approach correct?

No disparity is u2-u1 object coordinates is (u1,v1) in image1 and (u2,v2) in image2 It means that x axis for camera1 and camera2 are colinear

@LBerger: Sorry, I could not make myself clear in earlier post. I have attached a image to explain better. https://imgur.com/a/48jMI There are two real points (x',y') and (x,y), lying on the same plane which is parallel to camera plane. I understand disparity is inversely proportional to actual distance from camera. Now this actual distance is displacement from the real object point to optical center or perpendicular distance to camera plane? If it is actual distance, then disparity of these two points calculated would not be same, inspite of having constant distance from camera plane (perpendicular distance, will mean disparity of (x',y') (x,y) will be found same). I believe in this case I can use cosine of the horizontal angle cast w.r.t. to camera axis to bring all values to same scale.

@LBerger: I don't think a constant disparity means a sphere. As per literature that I have gone through, it seems disparity is inversely proportional to perpendicular distance from real world point to camera plane. Thus , a constant disparity means a plane held parallely to camera's plane.

Right that's not a sphere : Im'm tired it is written in equation Z=cste