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In camera imaging, there are several terms for point coordinates.

World coordinates: [X, Y, Z] in physical unit

Image coordinates: [u, v] in pixel.

Do these coordinates become homogeneous coordinates by appending with a 1? Sometimes in books and paper it is represented by [x, y w]. When is w is used? When is 1 used?

In the function initUndistortRectifyMap, http://docs.opencv.org/2.4/modules/imgproc/doc/geometric_transformations.html#void%20initUndistortRectifyMap(InputArray%20cameraMatrix,%20InputArray%20distCoeffs,%20InputArray%20R,%20InputArray%20newCameraMatrix,%20Size%20size,%20int%20m1type,%20OutputArray%20map1,%20OutputArray%20map2)

the following process is applied

enter image description here

Is there one term for the coordinates [x y 1]? I don't understand why R can be applied to [x y 1]? In my view, R is the transformation in 3D. Is [x y 1] is one 2d point or one 3d point?

[u v]->[x y]->[x y 1]->[X Y W]->[x' y'] The coordinates are processed according to the above chain. What is the principle behind it?

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