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The condition of the heart muscle tissue can be inferred by analyzing the time-intensity curves obtained with myocardial perfusion MRI. Specifically, identifying tissue that is under-supplied with blood is important when choosing a suitable therapy for patients with coronary heart disease. Before an analysis can be carried out, the images must be registered to compensate for cardiac and respiratory motion. This is a difficult problem, as the motion is non-rigid and because the image contrast varies strongly over time due to the injection of a contrast agent into the blood stream. To address these problems, an automatic non-rigid registration approach is presented that utilizes local phase instead of intensity or gradient information.