# camera pose rotation to local rotation for an object

Suppose I have the pose of an object in a 4 x 4 matrix (has translation and rotation information) but it's with respect to my camera frame Suppose I also have the intrinsic calibration off the camera that was used to find the pose of the object

Now I want to get the object rotation but in it's local coordinate system not in the camera frame coordinate system

What is the math to perform this transformation?

I have a feeling this is pretty easy to do but I just can't get my head around it. Is it something like the inverse of the camera intrinsic multiplied by 4 x 4 pose information?

Have a look at this (1.2.3 Homogeneous Transformations).

Sorry - I missed your comment so only seeing now. I had a read of the section you referred too but I'm struggling to make sense of it. I kind of understand it at a high level but not sure how to translate it to code. Would you be able to expand a little by way of a simple example - even some psuedo code would be really helpful? Thanks

When you have a

`4x4`

homogeneous transformation matrix that transforms a point expressed in frame B into the frame A, the inverse transformation is done using equation`(1.11)`

.