ALGORITHM 1.

Multi-resolution Regression Voting Algorithm

Input: Itest - a testing image with an unknown landmark position

ℛi, i = {Coarsest, ⋯, Finest} − ℛi is the regression forest trained in the i-th resolution

ρ0 - the voting neighborhood size for the 2nd coarsest resolution

Output: p - detected landmark position

Notations: 𝒩(x, ρ) - ρ-neighborhood of voxel x; 𝒩(Itest) - entire image domain of Itest

Initialization: ρ = ρ0

for i = Coarsest To Finest do

Re-sample image Itest to resolution i

/* Set the voting area Φ */

Φ = 𝒩(Itest)

if i ≠ Coarsest then

Φ = 𝒩(p, ρ)

ρ = ρ=2   /* Reduce the voting area by 23 in the next finer resolution */

end if

/* 3D displacement prediction */

for every voxel x in region Φ do

Predict the 3D displacement d̂(x) by regression forest ℛi

end for

/* Landmark voting */

Initialize voting map V to be zero and of the same size with Itest

for every voxel x in region Φ do

V (ROUND(x + d̂(x)) + = 1

end for

/* Landmark localization */

p = maxx V (x)

end for

Return p