A Fourier Domain Framework for Variational Image Registration

Image registration is a widely used task in image analysis, having applications in various fields. Its classical formulation is usually given in the spatial domain. In this paper, a novel theoretical framework defined in the frequency domain is proposed for approaching the multidimensional image registration problem. The variational minimization of the joint energy functional is performed entirely in the frequency domain, leading to a simple formulation and design, and offering important computational savings if the multidimensional FFT algorithm is used. Therefore the proposed framework provides more efficient implementations of the most common registration methods than already existing approaches, adding simplicity to the variational image registration formulation and allowing for an easy extension to higher dimensions by using the multidimensional Fourier transform of discrete multidimensional signals. The new formulation also provides an interesting framework to design tailor-made regularization models apart from the classical, spatial domain based schemes. Simulation examples validate the theoretical results.

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