Problem Interpreting Camera Calibration Matrix

[steven_mx]

Hi, I'm having a problem interpreting the camera calibration data found at http://www.cvg.cs.rdg.ac.uk/PETS2001/pets2001-cameracalib.html and was wondering whether anyone can help. Basically I understood the example and I it works correctly when I try to compute the 2D image coordinates of 3D objects. The 2D coordinates I get are within the image boundaries, which is good.

The problem is when I try to apply the working to the other matrices. To get you into perspective, these calibration matrices apply to the videos found at http://www.cvg.cs.rdg.ac.uk/PETS2001/pets2001-dataset.html

For example consider the transformation matrix of Dataset 2 Camera 2:

FocalLength f=792
ImageCentre (u,v) = (384, 288)
Homogeneous Transform T =

-0.94194 0.33537 -0.01657 0.00000
-0.33152 -0.93668 -0.11278 0.00000
-0.05334 -0.10073 0.99348 0.00000
11791.10000 22920.20000 6642.89000 1.00000

According to the instructions at the top of the dataset, the first step is to invert the matrix to get:

-0.94194 -0.33152 -0.05334 0
0.33538 -0.93669 -0.10074 0
-0.01657 -0.11277 0.99348 0
3529.67074 26127.15587 -3661.65672 1

Then take for example the point x = (0,0,0) in world coordinates.

xT = (3529.67074,26127.15587,-3661.65672) and the point in 2D coordinates is given by

(792 x 3529.67074 / -3661.65672 + 384, 792 x 26127.15587 / -3661.65672 + 288)
= (-763.45 + 384 , -5651.187 + 288)
= (-379.45, -5363.187)

Now this answer is clearly incorrect since the answer should be within the image boundaries. In fact when I tried to use this information in my program, points on the ground plane in the 3D world are transformed incorrectly into 2D image coordinates.

I would really appreciate if someone could give any idea on how to apply the working correctly.

Thanks,

Steven