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# 2D to 3D projection

Asked by bes on 28 Jun 2012

I have a 3D point cloud of an object (3D model) also i have photographs of that object and the camera parameters (focal length, angle) and location (gps location). from the photograph i have identified 2D coordinates (x,y) of some particular features . How can i project that 2D point in 3D surface to get 3D points of that corresponding feature? Thanks

Walter Roberson on 28 Jun 2012

Are there at least two photographs from different angles that contain each of the points to be identified?

You mention GPS: normal GPS has a positional accuracy of about 2-3 meters. If that is a significant fraction of the distances involved then this is going to present a calculation problem.

Richard Brown on 28 Jun 2012

I think a really good book for you to read if you want to understand what's going on geometrically is this one: http://www.amazon.com/Multiple-View-Geometry-Computer-Vision/dp/0521540518

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Answer by Richard on 28 Jun 2012

Your 2D points correspond to a ray in 3-space that passes through the 3D feature and the optical centre of the camera. You say you know the intrinsic parameters of the camera. So if you invert the camera's intrinsic calibration matrix, then you can place the image points on a 3D plane in the same Euclidean space as your point cloud. You then need to devise a way of finding the 3D point that's on (well, near actually) the ray emanating from the camera centre and passing through the image point on the image plane. Depending on the object in question this might be easy or quite difficult.

Hope that's useful in a vague sort of way. If you can be more specific, then we may be able to be of more help!

bes on 2 Jul 2012

thankyou

Richard Brown on 2 Jul 2012

If you send me an email with an image and the information you have, I'd be happy to have a quick look and point you in the right direction.

bes on 6 Jul 2012

In my image (Exif tag) it show dimention: 5184* 3456 width - 5184 pixels height - 3456 pixels horizontal and vertical resolution 240dpi bit depth- 24 camera model - Canon EOS 550D F-stop - f/3.5 exposure time 1/1000 sec focal length 18mm max aperture 3.625 subject distance - 4294967295m flash mode - no flash, compulsory 35mm focal length

It show 2 focal length. which one i have to use when calculating 3D? how to change the focal length in pixel coordinate?