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I have the intrisic and extrinsic parameters of the camera. The extrinsic is a 4 x 4 matrix with rotation and translation.

I have sample data as under, I have this one per camera image taken.

2.11e-001 -3.06e-001 -9.28e-001 7.89e-001 
6.62e-001 7.42e-001 -9.47e-002 1.47e-001 
7.18e-001 -5.95e-001 3.60e-001 3.26e+000 
0.00e+000 0.00e+000 0.00e+000 1.00e+000

I would like to plot the image as given on the Matlab calibration toolkit page Camera Centered or World centered However I'm unable to figure out the Math of how to plot these 2 images.

The only lead I have is from this page http://en.wikipedia.org/wiki/Camera_resectioning. Which tells me that the camera position can be found by C = − R` . T

Any idea how to achieve this task?

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1 Answer 1

up vote 2 down vote accepted

Assume the corners of the plane that you want to draw are 3x1 column vectors, a = [0 0 0]', b = [w 0 0]', c = [w h 0]' and d = [0 h 0]'.

Assume that the calibration matrix that you provide is A and consists of a rotation matrix R = A(1:3, 1:3) and a translation T = A(1:3, 4).

To draw the first view For every pose A_i with rotation R_i and translation T_i, transform each corner x_w (that is a, b, c or d) of the plane to its coordinates x_c in the camera by

x_c = R_i*x_w + T_i

Then draw the plane with transformed corners.

To draw the camera, its centre of projection in camera coordinates is [0 0 0]' and the camera x axis is [1 0 0]', y axis is [0 1 0]' and z axis is [0 0 1]'.

Note that in the drawing, the camera y-axis is pointing down, so you might want to apply an additional rotation on all the computed coordinates by multiplication with B = [1 0 0; 0 0 1; 0 -1 0].

Draw the second view Drawing the plane is trivial since we are in world coordinates. Just draw the plane using a, b, c and d.

To draw the cameras, each camera centre is c = -R'*T. The camera axes are the rows of the rotation matrix R, so for instance, in the matrix you provided, the x-axis is [2.11e-001 -3.06e-001 -9.28e-001]'. You can also draw a camera by transforming each point x_c given in camera coordinates to world coordinates x_w by x_w = R'*(x_c - T) and draw it.

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Wow! How did you do that, you are math wizard or something?! I'm sorry I can't understand much of it, so I will have to try it out practically. Thanks for the amazing reply!! –  Kevin Boyd Nov 19 '11 at 6:56

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