Matlab identify objects at boundary - matlab

Question

I know basic commands in order to identify objects in a picture like:
level = graythresh(bw);
bw = im2bw(bw,level);
cc = bwconncomp(bw, 4);
cc.NumObjects;
graindata = regionprops(cc, 'basic');
perimeter = regionprops(cc, 'perimeter');
Those codes above is the code I am using.
In the picture attached, I can get the number to be 4. So the code identify that there is in total 4 objects.
However, this picture actually contains two objects. If we replicate this picture and move the replicate to the up, down, left and right, we can see that there is only two objects. But they are "separated" by the boundary.
It is not doable to change the way of making the image so the only way I can think of is to use some function or codes in matlab.
I will really appreciate it if someone can provide some matlab function to solve this problem.

Answer 1

All you need to do is loop over the border rows and columns and merge any regions that line up on opposite sides. The following code will produce an image with the regions labelled by number in the way you want.
cc=bwconncomp(bw);
[rows,cols] = size(reg);
% matrix of region labels
regions = uint8(zeros(rows,cols));
% label each pixel with an integer for its region number
for i = 1:length(cc.PixelIdxList)
region(cc.PixelIdxList{i}) = i;
end
% loop over rows, merge the regions if pixels line up
for i = 1:rows
left = region(i,1);
right = region(i,end);
if (left>0) && (right>0) && (left~=right)
region(region==right) = left;
end
end
% loop over columns, merge the regions if pixels line up
for j = 1:cols
top = region(1,j);
bottom = region(end,j);
if (top>0) && (bottom>0) && (top~=bottom)
region(region==bottom) = top;
end
end