[WIP] Make ImageFiltering.imfilter pipeline differentiable

[SomTambe]

This PR aims to make the ImageFiltering.imfilter function differentiable.

• Add adjoints
• Get the gradient of the kernel
• Put tests

The current issue I am facing causes the gradient of the kernel to be nothing. There seems to be a place where I have incorrectly put a NoTangent(), or a @nograd. Infact upon some further tracing I found out it does go inside the rule of __imfilter_inbounds!, but never calls the pullback inside it.

julia> img = testimage("cameraman");

julia> gradf(x, k, args...) = Zygote.gradient((a, b)->imfilter(a, b, args...) |> sum |> (z->z.val), x, k)
gradf (generic function with 1 method)

julia> gradf(img, t*t') 
(Tangent{Gray{Float64}, NamedTuple{(:val,), Tuple{Float64}}}[Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,) … Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,); Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,) … Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,); … ; Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,) … Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,); Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,) … Tangent{Gray{Float64}}(val = 1.0,) Tangent{Gray{Float64}}(val = 1.0,)], nothing)

The img gradient is incorrect too, and I shall get it rectified when I write tests and figure out the kernel thing.

[codecov-commenter]

Codecov Report

Merging #21 (cf6fbf8) into main (890e927) will decrease coverage by 32.67%.
The diff coverage is 0.00%.

@@             Coverage Diff             @@
##             main      #21       +/-   ##
===========================================
- Coverage   88.23%   55.55%   -32.68%     
===========================================
  Files           3        4        +1     
  Lines         102      162       +60     
===========================================
  Hits           90       90               
- Misses         12       72       +60     

Impacted Files	Coverage Δ
src/filters/adjoints.jl	0.00% <0.00%> (ø)

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[DhairyaLGandhi]

Yeah you definitely want the Tangent to wrap an array and not elements I would imagine.

[DhairyaLGandhi]

Thanks for taking this up! Looking forward to the tests. I'll also take a look through the adjoints to see if they're correct

[DhairyaLGandhi]

Since it will be used further down in the computation pipeline, i think you still need to provide it the gradient so it can be accumulated properly. Else the answer would be incorrect

[DhairyaLGandhi]

Is this true generically?