Deformable Image Registration with Hyperelastic Warping

The extraction of quantitative information regarding growth and deformation from series of image data is of significant importance in many fields of science and medicine. Imaging techniques such as MRI, CT and ultrasound provide a means to examine the morphology and in some cases metabolism of tissues. The registration of this image data between different time points after external loading, treatment, disease or other pathologies is performed using methods known as deformable image registration. The goal of deformable image registration is to find a transformation that best aligns the features of a “template” and “target” image (Fig. 12.1). In the ideal case, the quantity and quality of the image texture present in the template and target images, as well as the similarity in underlying anatomical structure, would yield a unique “best” transformation. In real problems, however, this is not the case. Deformable image registration is most often ill-posed in the sense of Hadamard [2–3]. No perfect transformation exists, and the solution depends on the choice of the cost function and associate solution methods. Deformable image registration grew primarily out of the pattern recognition field where significant effort has been devoted to the representation of image ensembles (e.g., [4–13]). The approaches that are used are usually classified as either model-based or pixel-based. Model-based approaches typically require