Abstract. In this work we present a novel approach for elastic image registration of multi-phase contrast enhanced CT images of liver. A problem in registration of multiphase CT is that the images contain similar but complementary structures. In our application each image shows a dierent part of the vessel system, e.g., portal/hepatic venous/arterial, or biliary vessels. Portal, arterial and biliary vessels run in parallel and abut on each other forming the so called portal triad, while hepatic veins run independent. Naive registration will tend to align complementary vessel. Our new approach is based on minimizing a cost function consisting of a distance measure and a regularizer. For the distance we use the recently proposed normalized gradient field measure that focuses on the alignment of edges. For the regularizer we use the linear elastic potential. The key feature of our approach is an additional penalty term using segmentations of the dierent vessel systems in the images to avoid overlaps of complementary structures. We successfully demonstrate our new method by real data examples.