Algorithm 4.

Inferring 3D segmentation of cell nuclei

Require: $C_{3 D_final}$ : 3D array of final 3D cell regions with unique indices from Algorithm 3
Require: $N_{2 D}$ : 3D array of 2D nuclear regions from the Z-axis, each uniquely indexed at its Z-slice
1:	$N_{3 D_final}$ ← empty 3D array for final 3D nuclear regions
2:	final_indices ← list of unique indices of 3D cell regions in $C_{3 D_final}$
3:	for index in final_indices do
4:	{Iterate over each final 3D cell region}
5:	for $z$ in unique(where( $C_{3 D_final} [z, :, :] = = index$ )) do
6:	{Iterate over the Z-slices where the current 3D cell region exists}
7:	2D_region_coords ← where( $C_{3 D_final} [z, :, :] = = index$ )
8:	$C_{2 D}$ ⟵empty 2D array with the same XY dimensions as $C_{3 D_final}$ {Initialize array for individual final 3D cell region at slice z }
9:	$N_{2 D}$ ⟵ empty 2D array with the same XY dimensions as $C_{3 D_final}$ {Initialize array for individual final 3D nuclear region at slice z}
10:	$C_{2 D}$ [2D_region_coords] ← index {2D array with index value at the coordinates of current final 3D cell region at slice $z$ }
11:	$N_{2 D}$ [2D_region_coords] ← $N_{2 D}$ [ $z$ , 2D_region_coords] {2D array with indexed 2D nuclear regions overlapping with $C_{2 D}$ }
12:	if num(unique( $N_{2 D}$ ))> 1 then
13:	{If more than one nucleus is present}
14:	$N_{2 D}$ ⟵selectNucleus( $N_{2 D}, C_{2 D}$ )
15:	{Keep the nucleus with the smallest fraction beyond and on cell boundaries}
16:	end if
17:	$N_{2 D}$ ⟵trimNucleus( $N_{2 D}, C_{2 D}$ )
18:	{Remove nuclear pixels outside or on cell boundaries}
19:	$N_{3 D_final} [z, where(N_{2 D} \neq 0)]$ ← index
20:	{Store the trimmed 2D nuclear region}
21:	end for
22:	end for
23:	for index in final_indices do
24:	3D_region_coords ⟵ where ( $C_{3 D_final} = = index$ )
25:	{Get the 3D coordinates of the current final 3D cell region}
26:	num_overlap ⟵ findNucleus(3D_region_coords, $N_{3 D_final}$ )
27:	{Find the number of overlapping 3D nuclear regions}
28:	if num overlap = = 0 then
29:	$C_{3 D_final}$ [3D_region_coords] ← 0
30:	{Remove final 3D cell regions that do not have corresponding 3D nuclear region}
31:	end if
32:	end for