Image registration plays an important role in many cerebral image processing algorithms such as multi-modal image fusion, brain volumetry and parcellation, atlas-based morphometry, and so forth. The registration algorithms can be divided into the rigid and deformable categories. The former takes advantage of global rigid transformations (e.g. affine or rigid-body) while the later employ local deformable vector fields. In this paper, a novel deformable registration algorithm based on calculus of variations is proposed. Its energy functional consists of a second-order regulator term and an external energy functional based on the sum squared errors measure. The former makes the deformable vector field smooth and differentiable while the later increase the similarity between the wrapped moving image and fixed image by optimizing the vector field. Experimental results demonstrated superior performance of the proposed method for a large imagebase including 150 cerebral MPRAGE magnetic resonance images, in three categories of cognitively normal, mild cognitive inference, and Alzheimer disease.

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