🧹 Deprecate *diff difference functions in favor of fdiff

Four legacy methods are deprecated in favor of `ImageBase.fdiff`:

- `forwarddiffx`
- `forwarddiffy`
- `backdiffx`
- `backdiffy`

See the following two PRs for more information:

- JuliaImages/ImageBase.jl#11
- JuliaImages/ImageBase.jl#22

This commit bumps ImageBase compatibility to v0.1.5

Author: johnnychen94

src/Images.jl

@@ -140,10 +140,6 @@ export
     widthheight,
 
     # algorithms
-    backdiffx,
-    backdiffy,
-    forwarddiffx,
-    forwarddiffy,
     imcorner,
     imcorner_subpixel,
     corner2subpixel,

src/algorithms.jl

@@ -303,12 +303,6 @@ imgaussiannoise(img::AbstractArray{T}) where {T} = imgaussiannoise(img, 0.01, 0)
 
 # image gradients
 
-# forward and backward differences
-# can be very helpful for discretized continuous models
-forwarddiffy(u::AbstractMatrix) = [u[2:end,:]; u[end:end,:]] - u
-forwarddiffx(u::AbstractMatrix) = [u[:,2:end] u[:,end:end]] - u
-backdiffy(u::AbstractMatrix) = u - [u[1:1,:]; u[1:end-1,:]]
-backdiffx(u::AbstractMatrix) = u - [u[:,1:1] u[:,1:end-1]]
 function div(p::AbstractArray{T,3}) where T
     # Definition from the Chambolle citation below, between Eqs. 5 and 6
     # This is the adjoint of -forwarddiff
@@ -369,7 +363,7 @@ function imROF(img::AbstractMatrix{T}, λ::Number, iterations::Integer) where T<
     for i = 1:iterations
         div_p = div(p)
         u = img - λ*div_p # multiply term inside ∇ by -λ. Thm. 3.1 relates this to u via Eq. 7.
-        grad_u = cat(forwarddiffy(u), forwarddiffx(u), dims=3)
+        grad_u = cat(fdiff(u, dims=1, boundary=:zero), fdiff(u, dims=2, boundary=:zero), dims=3)
         grad_u_mag = sqrt.(sum(abs2, grad_u, dims=3))
         p .= (p .- (τ/λ).*grad_u)./(1 .+ (τ/λ).*grad_u_mag)
     end

src/deprecations.jl

@@ -1076,6 +1076,11 @@ function ColorVectorSpace.complement(x::AbstractArray)
     complement.(x)
 end
 
+@deprecate forwarddiffx(X) ImageBase.FiniteDiff.fdiff(X, dims=2, boundary=:zero)
+@deprecate forwarddiffy(X) ImageBase.FiniteDiff.fdiff(X, dims=1, boundary=:zero)
+@deprecate backdiffx(X) ImageBase.FiniteDiff.fdiff(X, dims=2, rev=true, boundary=:zero)
+@deprecate backdiffy(X) ImageBase.FiniteDiff.fdiff(X, dims=1, rev=true, boundary=:zero)
+
 # This is now replaced by ImageTransformations and Interpolations
 using ImageTransformations.Interpolations: BSpline, Linear, interpolate
 function bilinear_interpolation(img::AbstractArray{T,N}, xs::Vararg{<:Number, N}) where {T,N}

test/algorithms.jl

@@ -1,6 +1,7 @@
 using Images, OffsetArrays, TestImages
 using Statistics, Random, LinearAlgebra, FFTW
 using Test, Suppressor
+using ImageBase.FiniteDiff: fdiff
 
 @testset "Algorithms" begin
     @testset "Statistics" begin
@@ -471,7 +472,7 @@ using Test, Suppressor
         # Test that -div is the adjoint of forwarddiff
         p = rand(3,3,2)
         u = rand(3,3)
-        gu = cat(Images.forwarddiffy(u), Images.forwarddiffx(u), dims=3)
+        gu = cat(fdiff(u, dims=1, boundary=:zero), fdiff(u, dims=2, boundary=:zero), dims=3)
         @test sum(-Images.div(p) .* u) ≈ sum(p .* gu)
 
         img = [0.1 0.2 0.1 0.8 0.9 0.7;