Your axes will each have a 'Tag'. If you used Guide to create your GUI which I am guessing you did from the 'handles' usage then you will need to gather the axes handles together into an array by accessing them as e.g.
handles.hAxes = [ handles.axes1, handles.axes2, handles.axes3 ];
Then use
axes( handles.hAxes(m) )
to change axes.
Personally I favour:
imshow( returned_img, 'Parent', handles.hAxes(m) );
rather than explicitly changing the current axes with:
axes( handles.hAxes(m) )
but that should work too.