Calculating a transform with a circle and lines

I am trying to determine the transformation (rotation + translation + scale) between two images in order to shift them.

The images are taken with two different modalities that produce very different textures. So I can't use techniques based on maintaining the optical flow. I thought it would be nice to threshold the images to extract the geometries (see example below). But then I have trouble seeing what I could do...maybe extract the vertical lines and the central circle to help me extract my transformation.

I work in python, I looked at what Opencv could offer but with few success for the moment.

--- EDIT LATER ---

I detected the circle and lines with the Hough transform (see figure below). Indeed, this will help for a proper registration. However, what tool on Python can I use to register these elements? I often use optical flow conservation, but in this case it's rather complicated...

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