Finally, it is extremely important to note that all the mathematical algorithms
which we sketch lead to interactive procedures. This means that in each case
there is a human user in the loop (typically a clinical radiologist) who is the ultimate
judge of the utility of the procedure, and who tunes the parameters either on or
off-line. Nevertheless, there is a major need for further mathematical techniques
which lead to more automatic and easier to use medical procedures. We hope that
this paper may facilitate a dialogue between the mathematical and medical imaging
communities.