在OpenCV中从旋转矩阵和平移矢量获取旋转轴 [英] Obtain Rotation Axis from Rotation Matrix and translation vector in OpenCV

问题描述

我有两个图像的棋盘，它们有一定的旋转角度.让我们以第一张图片为参考找到第二张图片的旋转角度.

I have a chessboard in two images with some angle of rotation. Lets find the rotation angle of second image with reference of first image.

为此，我找到了这些对象的旋转矩阵(3x3)和平移矩阵(3x1).

For that I found the Rotation Matrix (3x3) and translation matrix (3x1) of those objects.

如何使用这些矩阵找到对象的旋转角度和旋转轴?

How can I find the Rotation Angle and Rotation Axis of object using those matrices?

推荐答案

对于旋转表示形式之间的每种转换类型，您都有此网站

For every type of conversion between rotation representations you have this website euclidean space.

您将找到以下方面的理论和代码示例:

You will find theory and code samples of:

• 四元数的旋转矩阵:链接

四元数到轴角:链接

一般的轮换和所有表示形式:链接

Rotations in general and all representations: link

关于您的问题，您有轴角度".如果您具有旋转矩阵R(3x3)，则可以通过这种方式获得角度和轴(请参见

And in relation to your question you have Axis Angle. If you have the rotation matrix R (3x3), you can obtain the angle and axis this way (see Matrix to Axis Angle):

• angle = acos(( R00 + R11 + R22 - 1)/2);

x，y，x轴:

x =(R21-R12)/sqrt((R21-R12)^ 2 +(R02-R20)^ 2 +(R10-R01)^ 2);

x = (R21 - R12)/sqrt((R21 - R12)^2+(R02 - R20)^2+(R10 - R01)^2);

y =(R02-R20)/sqrt((R21-R12)^ 2 +(R02-R20)^ 2 +(R10-R01)^ 2);

y = (R02 - R20)/sqrt((R21 - R12)^2+(R02 - R20)^2+(R10 - R01)^2);

z =(R10-R01)/sqrt((R21-R12)^ 2 +(R02-R20)^ 2 +(R10-R01)^ 2);

z = (R10 - R01)/sqrt((R21 - R12)^2+(R02 - R20)^2+(R10 - R01)^2);

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