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I have Intel T265 camera which has a camera coordinates system like following diagram: enter image description here

  • The camera system has two cameras and the center of the two cameras is the position of the camera system.

  • The point of my interest is P, which is translated from the position of the camera system by z0 along z axis, and x0 along x axis.

What I am given is a series of 4X4 (pose) matrices coming with the camera data looking like:

    0.9988    0.0175   -0.0466         0
   -0.0195    0.9989   -0.0426         0
    0.0458    0.0434    0.9980         0
   -0.0064   -0.0015   -0.0026    1.0000

or

   -0.1226    0.0055   -0.9924         0
   -0.0438    0.9990    0.0109         0
    0.9915    0.0448   -0.1223         0
   -0.2279   -0.0244    0.1860    1.0000

They look like homogenous matrix (following diagram) except that they are transposed version enter image description here

Now, I have a few questions about this 4x4 matrices:

  1. What is the position of the camera at each time point? Are they in these 4x4 matrices?
  2. Where exactly is the world coordinates and how is it oriented?
  3. How do I use these 4X4 matrices to find the projected position of point P in the world coordinates system?

Or do I misunderstand anything, and how should I use these matrices? Thank you.

I have tried P_w = M'*P_c, where P_c is the center of the camera system, and M' is the transpose of the matrices I am given, but the projected positions do not look right to me when I plot it.

Nick X Tsui
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  • Transposed in relation to what. What your used to? – joojaa Aug 01 '21 at 18:10
  • Usually a matrix is either row major or column major. The matrix in your example(with the red drawing) is column major. The matrix coming from the software appear to be row major. Look through the documentation to confirm if it is row or column major. For a row major matrix the translation is the last row instead of the last column. – pmw1234 Aug 01 '21 at 21:57
  • Actually I just checked and the matrix coming from the SDK is row major. (search for the word row in the documentation. So the translation in the first example is -0.0064 -0.0015 -0.0026 1.0000 – pmw1234 Aug 01 '21 at 22:00
  • @pmw1234 I'd think so. Do you also know the answer of my 2nd and 3rd questions? Thanks. – Nick X Tsui Aug 02 '21 at 10:39
  • If you'd think so, then the answer to the other questions seems self evident. – pmw1234 Aug 02 '21 at 11:05
  • @pmw1234 Please post an answer with some code so I can start testing. Thank you so much. – Nick X Tsui Aug 02 '21 at 11:13
  • Possibly of interest to you: https://computergraphics.stackexchange.com/a/6093/8009 describing the Object Space → World Space → Eye Space → Clip Space → Normalized Device Space → Window Space transformation and its inverse. – Wyck Aug 02 '21 at 13:58

0 Answers0