Applying OpenCV Pose Estimation to Blender Camera

Question

The Problem

I'm trying to use Blender to create synthetic image for use with OpenCV's pose estimation (specifically, OpenCV's findEssentialMat and recoverPose). However, I found that the rotation matrix R that OpenCV returns corrects for rotations along the camera's Y and Z axes, but not its X axis. I suspect this is because Blender and OpenCV have different camera models (see diagram), but I can't figure out how to correct for this. How would I take a rotation matrix made using OpenCV's camera model and apply it to Blender's camera model?

Additional Details

To test this, I rendered a scene from (0, 0, 30) using an identity camera rotation, then rotated the camera by 10 degrees along X, Y and Z. First, here's the identity rotation matrix (no rotation):

Here's a 10-degree rotation around X:

And here's a 10-degree rotation around Y:

Finally, here's a 10-degree rotation around Z:

Applying the rotation matrix OpenCV returns (for the estimated transformation between the rotated image and the original) corrects for all of these rotations except around X, which looks like this:

It seems that instead of correctly rotating by -10 degrees around X, the rotation matrix rotates a further 10 degrees around X.

Answer 1

Going from an OpenCV matrix to Blender could be accomplished by multiplying by another rotation matrix to compensate for the change in coordinates systems.

mat = [[1, 0, 0], 
       [0, -1, 0], 
       [0, 0, -1]]

You said the Y and Z components are already being compensated for so perhaps the negative of the matrix is what you need?