Abstract:

Image registration is one of the most challenging tasks within digital imaging. Given two images R and T, one is looking for a transformation y such that a deformed version T(y(x)) of T is similar to R. The problem arises, for example, when images taken from different objects, perspectives, times, or devices need to be compared or fused. Image registration, and 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. Current topics are the identification and treatment of characteristics of a particular application. A typical example is given by additional landmark constraints, enforcing a one-to-one match of so-called landmarks, i.e., outstanding corresponding points in the images.

In this talk, new approaches to constrained image registration and in particular to landmark constraints are considered and discussed. A general theoretical framework based on a variational approach is presented and supported by a numerical treatment, transferring constrained registration into a sequence of discrete constrained optimization problems. This not only leads to an efficient implementation but also raises and answers question on the interplay between a fixed number of constraints and the varying degrees of freedom arising through discretization.