Elastic, fluid, and diffusion registrations are sensitive to affine linear displacements. As a consequence, an affine linear pre-registration is unavoidable. The second order derivatives-based curvature regularizer is introduced to circumvent this additional pre-registration. The registration thus becomes less dependent on the initial position of reference and template images. For the practical implementation of the curvature registration, the continuous and discrete bi-harmonic equation are considered and numerical solution schemes are discussed. The natural relation to thin plate splines is shown. Various examples demonstrate the performance of curvature registration and the difference to elastic, fluid, and diffusion registration.
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