Does it look like this? Are these YOUR feet?
http://www.footvibe.co.uk/hard_skin.htm
:)
If it is - try this. Before bed, wash feet is warm water and use your pumice stone. Dry well, and slather LOTS of moisturising cream on - cheap stuff will do, E45 is good. Wrap each foot in a large piece of cling film and then put a sock on. This is to keep the cling film in place overnight.
You should see real improvements in a week - the clingfilm will help the cream to penetrate the skin, making it softer.
Obviously you will need to wash your feet each morning. :)
While you are doing this, try to wear natural socks - cotton or wool - and not open sandals outdoors with bare feet. You must keep your feet clean, dry and protected.