I have heard that shapeways indulge in converting 2d files to 3d printer compatible files for printing. I don't know if they still have this facility of 'image popper', but you should check that out. You can Try embossify.com too, it's free!
About sending a picture, yes you can send a file but again, if it's not a cad or a proper 3d compatible file then it creates problems.
May I know what kind of a picture it is? If it's human or a picture of a Cat, they have this thing called laser scanning, but the results are not always accurate; you can say that it's in its BETA stage. You'll have to take the Cat to the Lab for laser scanning or get her designed by a professional modeller. But you'll only find these in big companies and it would cost a lot.
Hope this helps.