I would like to perform the log-polar transform of an image. I tried. I failed. Maybe this is obvious to some of you…

First, I deal with the polar transform. The trouble seems to come from a specific type of images

using Revise
using CoordinateTransformations, ImageTransformation, Plots, TestImages, OffsetArrays
struct Retinotopy <: Transformation; end
struct InvRetinotopy <: Transformation; end
function (::Retinotopy)(x)
length(x) == 2 || error("Polar transform takes a 2D coordinate")
[(hypot(x[1], x[2])), atan(x[2], x[1])]
end
function (::InvRetinotopy)(x)
s,c = sincos(x[2])
( (x[1]) * c, (x[1]) * s)
end
Base.inv(::Retinotopy) = InvRetinotopy()
img = testimage("lighthouse")
tfm = Retinotopy()
# this works, Houra!
img0 = OffsetArray(img, -256:255, -384:383) # origin near top of image
imgw = warp(img0, tfm)
heatmap(imgw)
# this does not work !!!! What???
img = Gray.([(cos(x - y)) for x in LinRange(0,5pi,512), y in LinRange(0,5pi,768)])
img0 = OffsetArray(img, -256:255, -384:383); # origin near top of image
imgw = warp(img0, tfm)
heatmap(imgw)

@rveltz, not sure how the sampling is done but I think it is inevitable to have leftovers in this type of log-polar mapping, as both input and output from warp are rectangular. See code edited above. PS: btw, why the logarithm is not used in your definition?

@rveltz, I am sorry but my knowledge on this topic is small. I would only point out that if we do not offset the array, we get more wavefront rings but seemingly incomplete:

After some research on this, the results above do not seem to make sense.
The Polar-Cartesian transforms should wrap/unwrap images like posted here.
The simple code below adapted from Matlab seems to behave as expected for the Polar transform. It seems that you are looking for the inverse (Cartesian) transform. It might be easier to write it from scratch than to understand all the packages listed at the top of the post.

function imgpolarcoord(img::Array{Float64,2})
# Adapted from: Javier Montoya (2020). Polar Coordinates Transform, MATLAB Central File Exchange
# https://www.mathworks.com/matlabcentral/fileexchange/16094-polar-coordinates-transform
(rows,cols) = size(img)
cy, cx = rows ÷ 2, cols ÷ 2
radius = Int(minimum((cy,cx))) - 1
Nϕ = 4*360
Δϕ = 2pi/Nϕ
pcimg = zeros(radius + 1, Nϕ)
for j = 1:Nϕ, i = 1:radius+1
pcimg[i,j] = img[cy + round(Int,(i-1)*sin(Δϕ*(j-1))), cx + round(Int,(i-1)*cos(Δϕ*(j-1)))]
end
return pcimg
end
using ImageCore, Plots
N = 2000
img0 = ([ 0.5*(1.0 + cos(x-y)) for x in LinRange(0,5pi,N), y in LinRange(0,5pi,N)])
heatmap(Gray.(img0))
imgw = imgpolarcoord(img0)
imgw = ImageCore.n0f8(Gray.(imgw))
heatmap(imgw)
img0 = ([ 0.5*(1.0 + cos(hypot(x,y))) for x in LinRange(-4pi,4pi,N), y in LinRange(-4pi,4pi,N)])
heatmap(Gray.(img0))
imgw = imgpolarcoord(img0)
imgw = ImageCore.n0f8(Gray.(imgw))
heatmap(imgw)