Fourier-Net: Fast Image Registration with Band-Limited Deformation

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Unsupervised image registration commonly adopts U-Net style networks to predict dense displacement fields in the full-resolution spatial domain. For high-resolution volumetric image data, this process is however resource-intensive and time-consuming. To tackle this problem, we propose the Fourier-Net, replacing the expansive path in a U-Net style network with a parameter-free model-driven decoder. Specifically, instead of our Fourier-Net learning to output a full-resolution displacement field in the spatial domain, we learn its low-dimensional representation in a band-limited Fourier domain. This representation is then decoded by our devised model-driven decoder (consisting of a zero padding layer and an inverse discrete Fourier transform layer) to the dense, full-resolution displacement field in the spatial domain. These changes allow our unsupervised Fourier-Net to contain fewer parameters and computational operations, resulting in faster inference speeds. Fourier-Net is then evaluated on two public 3D brain datasets against various state-of-the-art approaches. For example, when compared to a recent transformer-based method, named TransMorph, our Fourier-Net, which only uses 2.2% of its parameters and 6.66% of the multiply-add operations, achieves a 0.5% higher Dice score and an 11.48 times faster inference speed. Code is available at https://github.com/xi-jia/Fourier-Net.