Conversion From Image to World Coordinates

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I am taking a depth map and converting it to a point cloud using an intrinsic matrix associated with the camera I have. Then using the X, Y, Z coordinates - I change the Z coordinate of certain points. Then I convert all coordinates back to image coordinates and a depth map. However, as I understand it, by changing even just the Z coordinate in the real world coordinates - I also change the u, v coordinates in the image space. How do I keep the image coordinates constant and only change the depth?

I have code which does this and I want to hold u,v constant through this transformation and only change Z/D.

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