I am trying to compute the gradient of a cost function defined as the Sum of Square Differences (SSD) between two images with respect to the parameters of an image transformation. In the code shown below, one of the images has been translated by a small amount. This is basically just a toy problem that I designed to understand if ForwardDiff.jl and ImageTransformations.jl play well together. Eventually, I will compute derivatives relative the parameters of different image warps:
using Images
using TestImages
using ImageTransformations
using ForwardDiff
img1 = testimage("cameraman.tif")
y_shift = 0.33
x_shift = -1.76
t = ImageTransformations.Translation(y_shift, x_shift)
img2 = ImageTransformations.warp(img1, t, ImageTransformations.indices_spatial(img1), 0)
function cost(Δ::Vector{T}) where T <: Real
t = ImageTransformations.Translation(Δ[2], Δ[1])
img2 = ImageTransformations.warp(img1, t, ImageTransformations.indices_spatial(img1), 0)
imgg1 = Gray.(img1)
imgg2 = Gray.(img2)
mat1 = convert(Array{Float64}, imgg1)
mat2 = convert(Array{Float64}, imgg2)
@. mat1 = (mat1 - mat2)^2
SSD = sum(vec(mat1))
return SSD
end
I’m getting this error:
StackOverflowError:
Stacktrace:
[1] make_typealias(x::Type)
@ Base ./show.jl:531
[2] show_typealias(io::IOBuffer, x::Type)
@ Base ./show.jl:661
[3] show(io::IOBuffer, x::Type)
@ Base ./show.jl:816
[4] show_datatype(io::IOBuffer, x::DataType)
@ Base ./show.jl:928
[5] show(io::IOBuffer, x::Type)
@ Base ./show.jl:819
[6] print(io::IOBuffer, x::Type)
@ Base ./strings/io.jl:35
[7] print_to_string(::String, ::Vararg{Any, N} where N)
@ Base ./strings/io.jl:135
[8] string
@ ./strings/io.jl:174 [inlined]
[9] floattype
@ ~/.julia/packages/FixedPointNumbers/HAGk2/src/deprecations.jl:4 [inlined]
[10] _default_digits(#unused#::Type{ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}) (repeats 43235 times)
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/autorange.jl:82
[11] __round(x::StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}})
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/autorange.jl:100
[12] (::ImageTransformations.var"#6#7"{Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}})(i::Int64)
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/autorange.jl:90
[13] iterate
@ ./generator.jl:47 [inlined]
[14] _collect
@ ./array.jl:691 [inlined]
[15] collect_similar
@ ./array.jl:606 [inlined]
[16] map
@ ./abstractarray.jl:2294 [inlined]
[17] _round(tform::CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}; kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/autorange.jl:89
[18] _round(tform::CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}})
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/autorange.jl:89
[19] warp!(out::Matrix{Gray{N0f8}}, img::Interpolations.FilledExtrapolation{Gray{N0f8}, 2, Interpolations.BSplineInterpolation{Gray{N0f8}, 2, Matrix{Gray{N0f8}}, Interpolations.BSpline{Interpolations.Linear}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}, Interpolations.BSpline{Interpolations.Linear}, Gray{N0f8}}, tform::CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}})
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/warp.jl:92
[20] warp(img::Interpolations.FilledExtrapolation{Gray{N0f8}, 2, Interpolations.BSplineInterpolation{Gray{N0f8}, 2, Matrix{Gray{N0f8}}, Interpolations.BSpline{Interpolations.Linear}, Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}}, Interpolations.BSpline{Interpolations.Linear}, Gray{N0f8}}, tform::CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}, inds::Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}})
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/warp.jl:88
[21] warp(img::Matrix{Gray{N0f8}}, tform::CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}, inds::Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}, args::Int64; kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/warp.jl:101
[22] warp(img::Matrix{Gray{N0f8}}, tform::CoordinateTransformations.Translation{StaticArrays.SVector{2, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}, inds::Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}, args::Int64)
@ ImageTransformations ~/.julia/packages/ImageTransformations/xYRLH/src/warp.jl:100
[23] cost(Δ::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}})
@ Main ./In[36]:18
[24] vector_mode_dual_eval(f::typeof(cost), x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}})
@ ForwardDiff ~/.julia/packages/ForwardDiff/QOqCN/src/apiutils.jl:37
[25] vector_mode_gradient(f::typeof(cost), x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}})
@ ForwardDiff ~/.julia/packages/ForwardDiff/QOqCN/src/gradient.jl:106
[26] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}, ::Val{true})
@ ForwardDiff ~/.julia/packages/ForwardDiff/QOqCN/src/gradient.jl:19
[27] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 2}}}) (repeats 2 times)
@ ForwardDiff ~/.julia/packages/ForwardDiff/QOqCN/src/gradient.jl:17
[28] top-level scope
@ In[37]:1
[29] eval
@ ./boot.jl:360 [inlined]
[30] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
@ Base ./loading.jl:1094
Any ideas? Thanks!