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this post also contributes to the post at Step by Step Camera Pose Estimation for Visual Tracking and Planar Markers by Jav_Rock (since I cannot add any comment there and I don't know why)

It can be seen that the translation vector 1x3 and rotation matrix 3x3 can be derived from homography matrix. However, the following question is: - where are the camera coordinate system and object coordinate system and how are they attached to the camera (or object)?? - there is the relative transformation between the two but the computation from homography or transformation matrix implies nothing about these coordinate systems' location & direction

Then, how to solve the pose estimation problem??

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The coordinate system you choose is completely arbitrary, as no information about real-world coordinates can be inferred. From an image of a table there is no reason to know that one leg is located at any particular $(X, Y, Z)$, or that it is any particular size (you can't tell if it's a doll's table or a giant's table).

Normally you would choose one of your cameras to be located at the origin, looking down the $z$ axis, defined by the matrix:

$$[R|t] = \begin{bmatrix} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \end{bmatrix}$$

Then due to the scale ambiguity you would have to choose an arbitrary scale, for example if you are using a stereo camera you could set the distance between the cameras to be one unit distance.

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  • $\begingroup$ I would not agree with the idea: from 1 image, pose cannot be derived. According to Zhang's method as I mentioned, the unknown pose & depth problem can be solved. The fact is, in his computation, the camera matrix is included as an additional information $\endgroup$ – Shawn Le Aug 28 '12 at 10:50

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