Rotation with FFT

Via shear it is possible to rotate an image. Shearing is basically a shift operation but with different shift distance in each row.

Examples

For full interactivity, have a look at this Pluto notebook.

using Revise, FourierTools, Plots, TestImages, PlutoUI, ImageShow

begin
    img = Float32.(testimage("fabio_512_gray"))
    z = zeros(Float32, (768, 768))
    FourierTools.center_set!(z, img)
end

Gray.(FourierTools.shear(z, -305))

Function references

FourierTools.shear — Function

shear(arr, Δ, shear_dir_dim=1, shear_dim=2)

Shears an array by the amount of Δ pixels via an FFT approach. Δ is the relative shift between the top and bottom row shifted with respect to each other. shear_dir_dim decides the direction of the shear and shear_dim is the second dimension where the shear happens. There is also shear! available.

For complex arrays we use fft, for real array we use rfft.

source

FourierTools.shear! — Function

shear!(arr, Δ, shear_dir_dim=1, shear_dim=2)

For more details see shear.

For complex arrays we can completely avoid large memory allocations. For real arrays, we need at least allocate on array in the fourier space.

source