  We propose a novel image registration method based on implicit neural
representations that addresses the challenging problem of registering a pair of
brain images with similar anatomical structures, but where one image contains
additional features or artifacts that are not present in the other image. To
demonstrate its effectiveness, we use 2D microscopy $\textit{in situ}$
hybridization gene expression images of the marmoset brain. Accurately
quantifying gene expression requires image registration to a brain template,
which is difficult due to the diversity of patterns causing variations in
visible anatomical brain structures. Our approach uses implicit networks in
combination with an image exclusion loss to jointly perform the registration
and decompose the image into a support and residual image. The support image
aligns well with the template, while the residual image captures individual
image characteristics that diverge from the template. In experiments, our
method provided excellent results and outperformed other registration
techniques.
