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is it possible to calculate a points 3D X and Y coordinate by inverting camera matrix

asked 2019-01-19 02:15:12 -0500

mikeitexpert gravatar image

updated 2019-01-19 03:25:30 -0500

LBerger gravatar image

I have read camera calibration explained.

I was able to do it with and just to test it i used this and everything is perfectly working.

I am just curious given the below equation and assuming I know the Z of a 3D point and its x,y pixel coordinates in the image, would I be able to assess the X, and Y coordinates of the 3D point?

In other words if I multiple the two sides of the equation by inv of camera matrix, and assuming I know the Z = w of a 3D point, then can I get the 3D X and Y of the point in 3D space?

![image description] (https://docs.opencv.org/2.4/_images/m...)

Any comments is much appreciate it.C:\fakepath\Selection_007.png

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answered 2019-01-19 05:45:51 -0500

Eduardo gravatar image

Yes you can. No need to invert the camera intrinsics matrix.

Perspective projection equations:

eq1

eq2

eq3


Reverse perspective projection equations assuming a known Z:

eq4

eq5

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Comments

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Thank you for valuable comment

I was wondering how would a small error in measurement of Z would distort the X and Y values assuming the is no error in measuring u and v.

Would you confirm it correlates with 1 / fx and 1/fy for X and Y direction? For my case it would be approximately 1/200.

I guess what I am trying to say is that the higher the fx and fy the lower detect we would experience from measuring Z/depth. Or simply the higher the resolution the more error we can tolerate introduced by measuring Z.

I hope it doesn't sound confusing. :)

Please let me know.

Regards

mikeitexpert gravatar imagemikeitexpert ( 2019-01-19 11:56:50 -0500 )edit
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Asked: 2019-01-19 02:15:12 -0500

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Last updated: Jan 19