In particular in medical imaging, registration schemes are known to be valuable
tools in various settings, like, e.g., the comparison of pre- and post biopsy
images. The currently available schemes in can roughly be divided in two
classes: landmark based and intensity based registration schemes. In this
paper, we present a rigorous mathematical framework for combining these two
techniques, in order to benefit from the advantages of both strategies.
Intensity based approaches aim to match images by minimizing an appropriate
distance measure, like, e.g., the $L_2$-norm of the difference image or the
mutual information of the two images. These techniques are generally full
automatic and yield a good registration on the average. However, they may
perform poorly for specific, important locations like anatomical landmarks. On
the opposite, landmark based registration techniques are designed to accurately
match user specified landmarks. A drawback of landmark based registration is
the fact that the intensities of the images are completely neglected.
Consequently, the registration result away from the landmarks may be very poor.
Here, we propose a mathematical framework for combining any distance measure
based registration with landmark information. We also present a general
numerical procedure for computing the wanted transformation as well as a
particular implementation for a specific distance measure based registration
technique. The general procedure computes a displacement field which is
mathematically guaranteed to produce a one-to-one match between given landmarks
and at the same time to minimize an intensity based measure for the remaining
parts of the images. The properties of the new scheme are demonstrated for a
variety of examples.
It is important to observe, that the presented novel technique for combining
intensity driven and landmark based approaches is independent on the two main