optimized mean filter using IntegralArrays

[johnnychen94]

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