  While hematoxylin and eosin (H&E) is a standard staining procedure,
immunohistochemistry (IHC) staining further serves as a diagnostic and
prognostic method. However, acquiring special staining results requires
substantial costs.
  Hence, we proposed a strategy for ultra-high-resolution unpaired
image-to-image translation: Kernelized Instance Normalization (KIN), which
preserves local information and successfully achieves seamless stain
transformation with constant GPU memory usage. Given a patch, corresponding
position, and a kernel, KIN computes local statistics using convolution
operation. In addition, KIN can be easily plugged into most currently developed
frameworks without re-training.
  We demonstrate that KIN achieves state-of-the-art stain transformation by
replacing instance normalization (IN) layers with KIN layers in three popular
frameworks and testing on two histopathological datasets. Furthermore, we
manifest the generalizability of KIN with high-resolution natural images.
Finally, human evaluation and several objective metrics are used to compare the
performance of different approaches.
  Overall, this is the first successful study for the ultra-high-resolution
unpaired image-to-image translation with constant space complexity. Code is
available at: https://github.com/Kaminyou/URUST
