optimized mean filter using IntegralArrays

When one needs to compute the sum/average of all blocks extracted from an image, pre-building the integral array usually provides a more efficient computation.

using BenchmarkTools, IntegralArrays

# simplified 3x3 mean filter; only for demo purpose
function mean_filter_naive!(out, X)
    Δ = CartesianIndex(1, 1)
    for i in CartesianIndex(2, 2):CartesianIndex(size(X).-1)
        block = @view X[i-Δ: i+Δ]
        out[i] = mean(block)
    end
    return out
end
function mean_filter_integral!(out, X)
    iX = IntegralArray(X)
    for i in CartesianIndex(2, 2):CartesianIndex(size(X).-1)
        x, y = i.I
        out[i] = iX[x±1, y±1]/9
    end
    return out
end

X = Float32.(rand(1:5, 64, 64));
m1 = copy(X);
m2 = copy(X);

@btime mean_filter_naive!($m1, $X); # 65.078 μs (0 allocations: 0 bytes)
@btime mean_filter_integral!($m2, $X); # 12.161 μs (4 allocations: 16.17 KiB)
m1 == m2 # true

One needs to specialize the mapwindow on mean function, e.g.,

function mapwindow(::typeof(mean), img, ...)
    ...
end

Start by reading the existing mapwindow entry point and its handling of mean operations, then compare its behavior with the IntegralArray example in the issue. The work is done when mean windows use the specialized path while preserving the existing results and interface; no specific file or test is named.