Algorithm 1.

Regression-based Hierarchical Deformation

Data: I - testing CT scan, 𝒟 - learned multi-task random   forest, and 𝒮init - initialized shape model
Result: 𝒮 - the final segmentation
Notation: World2Voxel(I, p) outputs voxel coordinate of vertex p on image I, 𝒟(I, x) returns the 3D displacement of voxel x on the image I, and Θ (K) denotes valid transform matrix set under transform type
K
Subroutine Deform(I, 𝒟, 𝒮, K)
	for Iteration ← 1 to MaxIteration do
		𝒮deform = 𝒮
		foreach vertex p ∈ 𝒮deform do
			x = World2Voxel(I, p)
			p = p + 𝒟(I, x)
		end
		if K ∈ {Translation, Rigid, Affine} then
			Estimate transform matrix T ∈ ℝ4×4:   argminT‖T (𝒮) − 𝒮deform‖2, s.t., T ∈ Θ (K)
			𝒮 = T (𝒮)
		else
			𝒮 = SmoothSurface(𝒮deform)
			𝒮 = RemeshSurface(𝒮)
		end
	end
	return 𝒮
Algorithm HierarchicalDeform (I, 𝒟, 𝒮init)
	𝒮 =Deform(I, 𝒟, 𝒮init, “Translation”)
	𝒮 =Deform(I, 𝒟, 𝒮,  “Rigid”)
	𝒮 =Deform(I, 𝒟, 𝒮,  “Affine”)
	𝒮 =Deform(I, 𝒟, 𝒮,  “FreeForm”)
	return 𝒮