Abstract.Image registration, in particular medical image registration, has been subject to extensive
studies in the past years. Its versatile and important applications have attracted researchers
from various branches, including numerical analysts. In this note, we not only give an
overview on some new and exiting approaches but also point out some of the mathemati-
cal challenges associated with these approaches. Moreover, we explain why variational based
methods to image registration naturally lead to large scaled and challenging optimization and
hence numerical linear algebra problems. We present various instructive examples and com-
ment on numerical schemes.