Determining pose of an object in 3d space

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Given a 3D model of an object centred at the origin, if I place a camera at position (x,y,z) and make it face the origin, from the image rendered the object appears to have changed its orientation (pose).

My question is, knowing the camera position how can I label the objects pose. i.e. how can I produce a rotation and translation matrix associated with the viewed pose?

For example, I am placing a virtual camera at each of the red nodes in the image below, for which I know their coordinates. My question is how do I define the camera or the object pose via a 4x4 transformation matrix? enter image description here

Thanks