# Connect bwlabeled components

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[EDIT: 20110623 22:06 CDT - reformat - WDR]

Hello, I need help on a very simple task...well..seemingly.

I have a series of images similarly to this: http://blogs.mathworks.com/images/steve/94/labeling_labeled_objects_03.png

except I have a tiff stack with numerous layers in series. In this image the blobs move around as one goes deeper into the tiff stack series (it is a spatial not temporal series). I am trying to do the following:

Find all unique objects per layer, connect objects from one plane to another that 'overlap'(thus indicating that both object x1 in layer a and x2 in layer b are the same object just at different spatial depths) as a line segment, generate a output with orientation in z of each line segment.

I have done the first instant. I am looking for advice on how to go about the object grouping, ie. connecting the same 'real object' in the serialized sections.

Any functions I should look at? Particle tracking functions perhaps?

Cheers,

##### 0 Comments

### Accepted Answer

Sean de Wolski
on 27 Jun 2011

Using bwconncomp on a three dimensional image will group them in 3d. You'll have to call it on each individual slice to see how many objects per slice there are:

sliceObjs = zeros(size(stack,3),1);

for ii = 1:size(stack,3)

CC = bwconncomp(stack(:,:,ii));

sliceObjs(ii) = CC.NumObjects;

end

EDIT This is a script, with the engine completely generalized and ready to go. I saved you above image; cropped it and translated it for visualization error checking purposes. The translation was done using my function FEX:imtranslate

%%Data and stuff

I = imread('ans627.png'); %your image

I = I(35:276,86:381,1)==255; %keep relevant part; convert to binary

I(:,:,2) = imtranslate(I,[10 -14]); %artificially translate for testing

I(5:11,270:275,2) = true; %add an eleventh object with no friends

szI = size(I);

Ds = cell(szI(3)-1); %preallocate place to store stuff

CCold = bwconncomp(I(:,:,1)); %cc of first slice

RPold = regionprops(CCold,'centroid');

centsA = vertcat(RPold(:).Centroid); %extract centroids

for ii = 1:(szI(3)-1)

CCnew = bwconncomp(I(:,:,ii+1)); %cc of next slice

RPnew = regionprops(CCnew,'centroid');

centsB = vertcat(RPnew(:).Centroid);

dim = 2; %which dimension will control in the bsxfun expression?

if CCold.NumObjects>CCnew.NumObjects

dim = 1;

end

%Engine:

xyDiff = bsxfun(@(x,y)abs(x-y),reshape(centsA,[],1,2),reshape(centsB,1,[],2)); %Centroids distances in each dimension

[~,idx] = min(hypot(xyDiff(:,:,1),xyDiff(:,:,2)),[],dim);

if dim==2;

displacements = centsB(idx,:)-centsA;

H = quiver(centsA(:,1),centsA(:,2),displacements(:,1),displacements(:,2));

else

displacements = centsB-centsA(idx,:);

H = quiver(centsB(:,1),centsB(:,2),displacements(:,1),displacements(:,2));

end

RPold = RPnew; %get ready to move on

CCold = CCnew;

centsA = centsB;

Ds{ii} = displacements; %can store other stuff too.

end

%SCd 06/27/2011

If you now look at displacements, you'll see that the artificial translation was recovered. I didn't place a threshold on distance - just used the minimum one. This could be added easily enough. (replace objects without a match to nan to maintain order)

### More Answers (3)

Wolfgang Schwanghart
on 24 Jun 2011

##### 2 Comments

Wolfgang Schwanghart
on 27 Jun 2011

Oh right. Somehow I thought bwconncomp works in 2D only, but I was wrong.

D
on 24 Jun 2011

##### 1 Comment

Sean de Wolski
on 24 Jun 2011

Yes - in 3D.

If you want the output structure identical to bwconncomp (for storage) purposes and you have a label matrix, you can use my label2CC function.

http://www.mathworks.com/matlabcentral/fileexchange/30702-label2cc

D
on 24 Jun 2011

##### 7 Comments

Sean de Wolski
on 27 Jun 2011

length(..) returns the size of the _largest_ dimension. Therefore, don't use it, since it's unreliable and can change!

force SIZE to output the size of the dimension you want, in this case 3, size(L,3);

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