# 2D pixel coordinate to 3D world coordinate conversion

Hii I want to convert pixel coordinates from an image to real world 3D coordinates . I have used camera calibration using a chessboard and have found Rotation Matrix , Translation matrix , Intrinsic matrix . What should be my next step for conversion ?? Essentially I want the 3D projection of a pixel of an image . Is it possible ?? Please Explain

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During the transformation from 3D to 2D you are losing the depth information. All you can do with the matrices that you have, is to transform a 2D pixel into a 3D line where every point on this line would be projected onto the same 2D pixel.

You will definitely need additional information to reconstruct a 3D point. For example an additional view of the same scene at the same time (stereo vision).

EDIT

The homography transforms one plane in 3D space into another plane in 3D space. You cannot get absolute coordinates from this, because the homography is not unique.

You can get some information from a single view, if you have some additional information about the view (if you have a calibration object in the view, or if you can use structured lighting, etc.)

I recommend searching for "single view geometry" and if you want to read an excellent book on this topic, I recommend "Multiple View Geometry in Computer Vision" by Hartley & Zisserman, which also has a chapter about single view geometry.

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What does HomographyMatrix*HomogeneousPixelCoordinates give ? I think the result would be world coordinates right ?? http://stackoverflow.com/questions/7836134/get-3d-coord-from-2d-image-pixel-if-we-know-extrinsic-and-intrinsic-parameters/10750648#10750648

( 2013-05-27 21:11:22 -0500 )edit

Is it possible to get 3D coordinates of the objects with a single camera ??

( 2013-05-28 03:28:12 -0500 )edit

( 2013-05-28 04:16:02 -0500 )edit

Heyy bjoernz thanx fr the quick reply :) I have one more query . What is the reference coordinate system ? We have formulae where we substitute the pixel coordinates and get the world coordinates , What is the reference coordinate system ??

( 2013-05-28 04:23:04 -0500 )edit

Hi, you can check this website Make3D. In this project they trained a machine learning algorithm that can estimate depth from just one image.

Regards.

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