To shift an image by a subpixel offset, it is necessary to use resampling methods. Provided some assumptions about the input signal cut-off frequency, an image is considered as the discretization of a continuous band-limited signal. According to Shannon's theorem, it is possible to retrieve completely this continuous signal from the knowledge of enough samples. It is then easy to resample the image, i.e. construct a new image with samples taken a new position of interest, namely the required offset. Interested readers are referred to [Wolberg 90].
Designing an interpolation kernel can either be done in image or Fourier space. There is no best kernel for all purposes, but rather a zoo of possible filters, the output quality depending on the frequency contents of the input signal.
In the present implementation, we chose to resample images in the image space. The interpolation kernel is based on the 16 closest pixel values, there are 6 offered interpolation kernels described here.