Format of parameters in KITTI's calibration file

Question

I accessed calibration files from part odometry of KITTI , wherein contents of one calibration file are as follows:

P0: 7.188560000000e+02 0.000000000000e+00 6.071928000000e+02 0.000000000000e+00 0.000000000000e+00 7.188560000000e+02 1.852157000000e+02 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 0.000000000000e+00
P1: 7.188560000000e+02 0.000000000000e+00 6.071928000000e+02 -3.861448000000e+02 0.000000000000e+00 7.188560000000e+02 1.852157000000e+02 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 0.000000000000e+00
P2: 7.188560000000e+02 0.000000000000e+00 6.071928000000e+02 4.538225000000e+01 0.000000000000e+00 7.188560000000e+02 1.852157000000e+02 -1.130887000000e-01 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 3.779761000000e-03
P3: 7.188560000000e+02 0.000000000000e+00 6.071928000000e+02 -3.372877000000e+02 0.000000000000e+00 7.188560000000e+02 1.852157000000e+02 2.369057000000e+00 0.000000000000e+00 0.000000000000e+00 1.000000000000e+00 4.915215000000e-03
Tr: 4.276802385584e-04 -9.999672484946e-01 -8.084491683471e-03 -1.198459927713e-02 -7.210626507497e-03 8.081198471645e-03 -9.999413164504e-01 -5.403984729748e-02 9.999738645903e-01 4.859485810390e-04 -7.206933692422e-03 -2.921968648686e-01

I can get that P0, P1 represent monochrome camera and P2, P3 color camera. To my understanding, common shape of camera intrinsic is

fx 0  cx
0  fy cy
0  0  1 .

So I cannot figure out the meaning of remaining three parameter (I guess used for distortion rectification) in each line and the last line following label Tr .

A similar question can be found from this post , but answers to it are still unobvious to me. Can anyone help me out?

Answer 1

In those files, P1 , P0 etc are not camera intrinsics but projection matrices, defined by something like

P1=calibration_matrix * [R_1 | T_1]  

which means that they are of size 3*4 . I'm not exactly sure whether the corresponding definition is the one above or if you'll have to use (well, it's an equivalent definition, more or less...)

P1=calibration_matrix*[R_1.transpose() | -R_1.transpose()*T_1] 

but I think that it's easy to check this by just reading/displaying the data.

As for Tr , it is the concatenation of all camera positions. You have four cameras P0, ..., P3 , and Tr has 12 elements, so the first three are the translation of P0 , the next three are the translation of P1 and so on. What I'm not sure about is whether each of those are expressed as T_i or -R_i.transpose()*T_i . I think the safest way is try to check this by playing with the data.

As for why there are four cameras P0, ...,P3 , to quote their paper :

Here, i ∈ { 0 , 1 , 2 , 3 } is the camera index, where 0 represents the left grayscale, 1 the right grayscale, 2 the left color and 3 the right color camera.

I think that also explains why their projection matrices are close to each other.

Answer 2

Those are baselines in meters wrt the reference camera 0.

This post has more details: How Kitti calibration matrix was calculated?