Algorithm 3 [Multiresolution multiscale active masks]

Input: Image f, initial number of masks M, initial resolution level K, scale of the region-based lowpass filter a, scale of the voting-based lowpass filter b, skewing factor α, harshness of the threshold β, average border intensity γ.

Output: Collection of masks ψ and final iteration number i.

MRMSActiveMasks(f, M, K, a, b, α, β, γ)

Initialization

i = 0, k = K, j = 1, ${\psi }_0^{(k,j)}(n)=\text{rand}(M)$, I = f

Multiresolution block

while k ≥ 0 do

Compute coarse version of the image

f(n) = Hk I (n)

Multiscale block

while j ≤ Jk do

Basic block

$({\psi }_p^{(k,j)},p)=\mathbf{\text{ActiveMasks}}(f,M,{\psi }_0^{(k,j)},a_{k,j},b,\alpha ,\beta ,\gamma )$

Change of scale parameter at resolution k

${\psi }_0^{(k,j+1)}(n)={\psi }_p^{(k,j)}(n)$

j = j + 1, i = i + p

end while

Lift mask ψ to the next higher resolution k − 1

${\psi }_1^{(k-1,1)}(n)={\psi }_p^{(k,j-1)}(\lfloor 2^{-1}n\rfloor )$

k = k − 1

end while

return (ψ, i)