Obtain Rotation Axis from Rotation Matrix and translation vector in OpenCV

Question

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.

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

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

Solution 1

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

You will find theory and code samples of:

• Rotation matrix to quaternion: link

• Quaternion to axis angle: link

• Rotations in general and all representations: link

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);

• Axis x,y,x:

  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);

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

Solution 2

Already working wih openCV I would rcommend using the Rodrigues method: cv::Rodrigues(src, dst, jacobian), that computes the rotation vector if you have a rotation matrix for an argument and vice versa.

Comments

[aranga]

Hi..jav i have a another one question.my object was placed parallel to a wheel.when the wheel is moving,my object also moved using the rotation matrix i was calculated the angle and rotation axis.Now the question is,how to calculate the rotation angle of the wheel center or spindle.i47.tinypic.com/344vck6.jpg