Color image support

[johnnychen94]

Cont. #14

metrics from Distances.jl needed to be tested to support color image inputs.

Unless explicitly stated, the distances are the sum of channelwise distances, and mean/normalized distances are divided by num_pixel*num_channel.

That's to say, ssdn in Images.jl is not defined correctly for Color3 Images

"`s = ssdn(A, B)` computes the sum-of-squared differences over arrays/images A and B, normalized by array size"
ssdn(A::AbstractArray{T}, B::AbstractArray{T}) where {T} = ssd(A, B)/length(A)

cc @timholy

[timholy]

Is it clear one wants to divide by num_channel? Why? After all, if you're computing the distance between two points in 3 dimensions, you don't divide by 3.

[johnnychen94]

🤔 I guess I need to document the behavior dist(channelview(a), channelview(b)) != dist(a, b) for Color3 Images

[johnnychen94]

A perhaps surprising result of not channelview Color3 images is the inequality of Minkowski(2) and Euclidean()...

julia> x = rand(RGB{N0f8}, 4, 4)

julia> y = rand(RGB{N0f8}, 4, 4)

julia> evaluate(Euclidean(), x, y)
2.6403928f0

julia> evaluate(Minkowski(2), x, y)
3.9360266173004748

This is because Minkowski(2) uses abs(xi - yi).^2 while Euclidean() uses abs2(xi - yi).

Can we do more than just documenting these seeming strange behaviors?

[johnnychen94]

Ref: JuliaGraphics/ColorVectorSpace.jl#126