Fourier Image Manipulation Tools¶
There are a few interesting Fourier-based image manipulation tools implemented in this package.
Shift Theorem¶
The Fourier shift theorem allows an image to be shifted in any directions by an arbitrary amount, including sub-pixel shifts. It is more computationally efficient than most interpolation techniques (or at least, so I think). It is described well in this lecture and in the NRAO interferometry course.
The shift code is in image_registration.fft_tools.shift
.
Similarity Theorem¶
The similarity theorem, or scale theorem, allows you to upsample timestreams. You cannot gain information below the image scale, but it is useful for getting sub-pixel information about gaussian peaks, for example. This NRAO lecture details the math.
The zoom and upsample methods are in image_registration.fft_tools.scale
and image_registration.fft_tools.zoom
.
Resources¶
I made use of a lot of not particularly easy to find documents when writing this code.
As stated elsewhere, though, the main inspiration for this work was Manuel Guizar’s DFT upsampling technique