How to create an interactive 3D axis

I have this vision in my mind that I would hope it could be possible.

So consider the following image which I let MATLAB read

I want to know if there's a code where a user has to define a 3D axis by identifying 4 points on the figure like this :

After the user plots these points, MATLAB should create a 3D axis that connects these points as follow :

Once this is accomplished MATLAB should take this axis reference into account if a user wishes to identify points on this image where MATLAB should calculate (x,y,z) coordinates with respect to the origin that the user had identified earlier.

I would be really grateful if such algorithm is possible to make and I would be happy for any suggestions