Algorithm 1.

Initial ROI Segmentation

1:	Inputs: seed set S, filtered image I
2:	// Initialize data structures
3:	for all p ∈ I do
4:	Compute F (p) using (10–11)
5:	if p ∈ S then
6:	T (p) = 0, R(p) = 1
7:	else
8:	T (p) = ∞, R(p) = 0
9:	S → ℒ // Begin the heap
10:	Tc = To = 0
11:	while ℒ ≠ ∅ do
12:	// Make heap’s top pixel, which has min T (p), alive
13:	pop(ℒ) → p, Alive(p) = TRUE
14:	Tc = T (p), ΔR = 0
15:	// Locate pixels constituting R
16:	if Tc − To ≥ 2 then
17:	TR = To + 1
18:	for all q ∈ I such that R(q) ≠ 1 do
19:	if T (q) ≤ TR then
20:	R(q) = 1
21:	exit
22:	else if Tc − To ≥ 1 then
23:	TR = Tc
24:	for all q ∈ I such that R(q) ≠ 1 do
25:	if T (q) ≤ TR then
26:	R(q) = 1, ΔR = ΔR + 1
27:	if ΔR ≤ Δmin then
28:	exit // Avoid potential ROI leakage
29:	else
30:	To = Tc
31:	// Check 4-neighbors of p
32:	for all q ∈ 𝒩(p) such that ¬Alive(q) do
33:	Compute T (q) using (eq:FastMarching) // Update arrival time
34:	if q ∉ ℒ then
35:	q → ℒ // Add to heap
36:	heap-sort(ℒ) // Resort the heap
37:	fill-holes(R) → R // Fill holes in final output
38:	return R