Multi-phase segmentation of a rock core

I am currently working with microCT images of rocks, more specifically cores (like the following image)

Since the acquisition is done by the lab operator, the images he gives me have some problems

Which is not wrong, but it is not the desire. I tried with scissors, but since the core is inclined, I can’t do it.

I would be grateful if you could guide me.

You should be able to threshold the air outside the rock first, then when you do the inside of the rock don’t let it overwrite the air.