KITTI校准文件中的参数格式 [英] Format of parameters in KITTI's calibration file

问题描述

我从 KITTI的部分里程表中访问了校准文件，一个校准文件如下：

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

我可以得出P0，P1代表单色相机，P2，P3彩色相机。据我了解，相机固有的常见形状是

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 .

所以我无法弄清楚每个参数中剩下的三个参数（我猜是用于失真校正）的含义行和标签 Tr 之后的最后一行。

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.

类似的问题可以从这篇文章，但是对我来说答案仍然不明显。有人可以帮我吗？

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

推荐答案

在这些文件中， P1 ， P0 等不是相机内在函数，而是投影矩阵，由类似以下内容定义

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

P1=calibration_matrix * [R_1 | T_1]  

这意味着它们的大小为 3 * 4 。我不确定相应的定义是否是上面的定义，或者您是否必须使用（嗯，这是一个等效的定义，或多或少...）

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] 

，但我认为通过阅读即可轻松检查/显示数据。

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

对于 Tr ，它是所有摄像机位置的串联。您有四个摄像机 P0，...，P3 ，而 Tr 的摄像机 12 元素，因此前三个是 P0 的翻译，接下来的三个是 P1 等等。我不确定的是每个参数都表示为 T_i 还是 -R_i.transpose（）* T_i 。我认为最安全的方法是尝试通过处理数据进行检查。

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.

至于为什么有四个摄像机 P0，...， P3 ，引用其论文：

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

此处
i
∈
{
0
，
1
，
2
，
3
}
是相机索引，其中
0
代表$ b左边的灰度是$ b，右边的灰度是
1
，左边是
2
，右边是彩色相机
3
。

我认为这也解释了为什么它们的投影矩阵彼此接近。

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

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