Coordinate Transforms
This paper describes an FFT-like algorithm in Polar coordinate-space
Fast and Accurate Polar Fourier Transform
A. Averbuch, R.R. Coifman, D.L. Donoho, M. Elad, M. Israeli 01-12-2004
Neat idea I think and pretty clear paper too.
I think of it as sort of folding a square grid on itself. You can get down to eight triangles 45 degree before the points in each grid don't lie exactly on top of each other.
So cartesian fft of that folded space can be inverted with no loss of information.
In the end though rotate and reflect is a lot of iteration and might be slow compared to fft of a warped space which is how -blur_radial and -blur_angular work in GMIC. I did try using -pde_flow to make comparisons of the "interpolation" and odd "pixel shape" noise but that's really slow for any decent amount of blur.
So would be nice not to explicitly transform coordinates back and forth.
That final bit to make a frequency domain radial and angular is nearly linear locally.
Must have a try but job #1 is to get on and make a wiki.
Fast and Accurate Polar Fourier Transform
A. Averbuch, R.R. Coifman, D.L. Donoho, M. Elad, M. Israeli 01-12-2004
Neat idea I think and pretty clear paper too.
I think of it as sort of folding a square grid on itself. You can get down to eight triangles 45 degree before the points in each grid don't lie exactly on top of each other.
So cartesian fft of that folded space can be inverted with no loss of information.
In the end though rotate and reflect is a lot of iteration and might be slow compared to fft of a warped space which is how -blur_radial and -blur_angular work in GMIC. I did try using -pde_flow to make comparisons of the "interpolation" and odd "pixel shape" noise but that's really slow for any decent amount of blur.
So would be nice not to explicitly transform coordinates back and forth.
That final bit to make a frequency domain radial and angular is nearly linear locally.
Must have a try but job #1 is to get on and make a wiki.
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