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Add Butterworth Filter #242

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f00d04e
add butterworth codes
ashwinn-v Jan 17, 2022
b6a98ca
add butterworth func
ashwinn-v Jan 17, 2022
228207e
Update src/kernel.jl
ashwinn-v Jan 17, 2022
e10c1b0
minor changes
ashwinn-v Jan 17, 2022
a848ed0
Docs and Tests
ashwinn-v Jan 17, 2022
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2 changes: 1 addition & 1 deletion src/ImageFiltering.jl
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Expand Up @@ -72,7 +72,7 @@ ArrayLike{T} = Union{ArrayType{T}, AnyIIR{T}}

include("kernel.jl")
using .Kernel
using .Kernel: Laplacian, reflect, ando3, ando4, ando5, scharr, bickley, prewitt, sobel, gabor, moffat
using .Kernel: Laplacian, reflect, ando3, ando4, ando5, scharr, bickley, prewitt, sobel, gabor, moffat, butterworth

NDimKernel{N,K} = Union{AbstractArray{K,N},ReshapedOneD{K,N},Laplacian{N}}

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20 changes: 20 additions & 0 deletions src/kernel.jl
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Expand Up @@ -509,6 +509,26 @@ moffat(α::Real, β::Real) = moffat(α, β, ceil(Int, (α*2*sqrt
sum(x.^2)
end

"""
butterworth(n,Wn,ls{tuple}) -> k
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@johnnychen94 johnnychen94 Jan 20, 2022

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indentation, and :: for type annotation.

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butterworth(n,Wn,ls{tuple}) -> k
butterworth(n, Wn, ls::Dims) -> k

Returns a multidimensional dimensional Butterworth kernel contained in an OffsetArray(::Matrix{Float64})
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@johnnychen94 johnnychen94 Jan 20, 2022

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one extra new line after the signature.

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Returns a multidimensional dimensional Butterworth kernel contained in an OffsetArray(::Matrix{Float64})
Returns a multidimensional dimensional Butterworth kernel contained in an OffsetArray(::Matrix{Float64})


- `n` is the order of the filter
- `Wn` is the normalized cutoff frequency
- `ls` is the size of the kernel
Comment on lines +516 to +518
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@johnnychen94 johnnychen94 Jan 20, 2022

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You don't need indentation for the markdown list

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- `n` is the order of the filter
- `Wn` is the normalized cutoff frequency
- `ls` is the size of the kernel
- `n` is the order of the filter
- `Wn` is the normalized cutoff frequency
- `ls` is the size of the kernel

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@johnnychen94 johnnychen94 Jan 20, 2022

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why you use ls for kernel size instead of sz? The former seems to come from the math equation of butterworth kernel. Can you also add the equation to the docstring so that people immediately knows what n, Wn, ls means and how they affects the results?

#Citation
Selesnick, Ivan W., and C. Sidney Burrus. "Generalized digital Butterworth filter design." IEEE Transactions on signal processing 46.6 (1998): 1688-1694.
"""

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@johnnychen94 johnnychen94 Jan 20, 2022

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Extra empty line here would cause ?Kernel.butterworth giving nothing.

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function butterworth(n::Real, Wn::Real, ls::Tuple{Integer,Integer})
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@johnnychen94 johnnychen94 Jan 20, 2022

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It looks like if we do

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function butterworth(n::Real, Wn::Real, ls::Tuple{Integer,Integer})
function butterworth(n::Real, Wn::Real, ls::NTuple{N,Integer}) where N

we immediately get a N-dimensional implementation as the docstring says: "multidimensional dimensional Butterworth kernel". Can you check this and if it works, add 1d and 3d tests? Also don't forget to update the docstring OffsetArray(::Matrix{Float64}).

ws = map(n->(ceil(Int,n)>>1), ls)
R = CartesianIndices(map(w->IdentityUnitRange(-w:w), ws))
nn = 2*n
@. 1/(1+(sqrt(2)-1)*(df(R)/Wn)^nn)
end

butterworth(n::Real, Wn::Real, ls::Integer) = butterworth(n, Wn, (ls,ls))
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@johnnychen94 johnnychen94 Jan 20, 2022

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This convenient method only makes sense when butterworth is 2D only; otherwise, we should not add it.


"""
reflect(kernel) --> reflectedkernel

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8 changes: 8 additions & 0 deletions test/specialty.jl
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Expand Up @@ -238,6 +238,14 @@ using ImageFiltering: IdentityUnitRange
fwhm = ceil(Int, (α*2*sqrt(2^(1/β) - 1)) * 4)
@test Kernel.moffat(α, β) == Kernel.moffat(α, β, (fwhm, fwhm))
end

@testset "butterworth" begin
a = rand()
b = rand()
@test Kernel.butterworth(a,b,(3,3)) == Kernel.butterworth(a,b,3)
@test Kernel.butterworth(a,b,(4,4)) == Kernel.butterworth(a,b,4)
Comment on lines +245 to +246
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@johnnychen94 johnnychen94 Jan 20, 2022

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We also need some numerical tests here, can you test against one or two results generated from other frameworks that has butterworth implemented or manual calculated results? Also do remember to add a comment on how the references are generated.

We also need to test that the kernel axis are "centered". For instance, the axes should be (-1:1, -1:1) when kernel size is (3, 3). Also need to test the even case as well.

end

end

nothing