如何从矩阵计算角度 [英] How to calculate the angle from Roational matrix

问题描述

我使用单个对象的两个图像对象与其第一个图像有一定程度的匹配。

我计算了每个图像的POSE，并使用Rodergues（）将旋转向量转换为Matrix， 。现在我如何计算并看到它从第一个位置旋转多少？
$ $ $ $
i尝试了很多方法，但答案是没有关闭_
编辑：我的相机是固定的对象正在移动

解决方案

我们可以使用以下公式从旋转矩阵中获取欧拉角。

给定一个3×3旋转矩阵

3个欧拉角度

这里atan2是相同的反正切函数，有象限检查，通常在C或Matlab中找到。 / p>

注意：如果围绕y轴的角度正好是+/- 90°，则必须小心。在这种情况下，第一列和最后一行中除了下角的一个（1或-1）之外的所有元素将为0（cos（1）= 0）。一种解决方案是将围绕x轴的旋转固定为180°，并从以下位置计算围绕z轴的角度：atan2（r_12，-r_22）。

另请参见 http://www.soi.city.ac.uk /~sbbh653/publications/euler.pdf

I am using two image of the single object the object is roated certain degree from its first image.
And i have calculated the POSE of each image and converted the rotational vector to Matrix using Rodergues(). Now how do i calculate and see how much it is rotated from its first position?
i have tried many ways but answers was no were close
EDIT: My camera is Fixed only the object is moving

解决方案

We can get euler angles from rotation matrix using following formula.

Given a 3×3 rotation matrix

The 3 Euler angles are

Here atan2 is the same arc tangent function, with quadrant checking, you typically find in C or Matlab.

Note: Care must be taken if the angle around the y-axis is exactly +/-90°. In that case all elements in the first column and last row, except the one in the lower corner, which is either 1 or -1, will be 0 (cos(1)=0). One solution would be to fix the rotation around the x-axis at 180° and compute the angle around the z-axis from: atan2(r_12, -r_22).

See also http://www.soi.city.ac.uk/~sbbh653/publications/euler.pdf

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