Masked FFT registration

Registration is a ubiquitous task for image analysis applications. Generally, the requirements of registration algorithms include fast computation and large capture range. For these purposes, registration in the Fourier domain using normalized cross correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain. We also provide an extension of this masked registration approach from simple translation to also include rotation and scale. We demonstrate the computational efficiency of our algorithm and validate its correctness on several synthetic images and real ultrasound images. Our framework enables fast, global, parameter-free registration of images with masked regions.