How to calculate the distance, in pixels, between each centroid in a binary image.

Hi All,

In short, my question is, "how do you calculate or find out the distance in pixels, between each centroid in a binary image?". I have looked at numerous other questions and can't seem to find one that explains it in a way that I can understand. I am relatively new to Matlab (2 months to be exact, with no previous experience in any other computer language). I have attached the "original image (unprocessed)", the "binary (and rotated) figure", and the "cropped binary figure" I am working with.

I have plotted the centroids onto the cropped binary image using this code:

a1RP=regionprops(a1C,'Centroid','MajorAxisLength',...
    'MinorAxisLength','Orientation', 'Eccentricity'); 
CentroidS=cat(1,a1RP.Centroid);
figure 
imshow(a1C)
hold on 
plot(CentroidS(:,1),CentroidS(:,2),'b*')
hold off

which, gives the following figure: attached as "binary image with plotted centroids"

I have tried pdist() and pdist2() but I don't understand what the output means. I get a 100x100 double output, and I am not sure how to interpret that. The code I used for that is as follows:

CentroidDistances=pdist2(CentroidS(:,1),CentroidS(:,2),'euclidean');

The reason I want to know the distance between each centroid is because I want to know what the pitch is, in the grid I am imaging, in pixels. The pitch is ~64 microns, but I want to know how many pixels in the image, correspond to 64 microns, and I think the distance between each neighbouring centroid would give me that. In my mind, I expected each of these distances to be the same, but the 100x100 array threw me off.

I really hope I am making sense. If I am not, please feel free to ask me to clarify or expand, if you want more detail

Thank you.

P.s. This is the full code I used:

imshow(a1) % a1=original image (unprocessed)
a1G=mat2gray(a1); 
a1GC=imadjust(a1G); 
a1GCT=graythresh(a1GC); 
a1B=imbinarize(a1GC,a1GCT); 
a1R=imrotate(a1B,17,'nearest','loose'); 
a1C=imcrop(a1R); 
a1RP=regionprops(a1C,'Centroid','MajorAxisLength',...
    'MinorAxisLength','Orientation', 'Eccentricity'); 
CentroidS=cat(1,a1RP.Centroid); 
figure 
imshow(a1C)
hold on 
plot(CentroidS(:,1),CentroidS(:,2),'b*')
hold off 
CentroidDistances=pdist2(CentroidS(:,1),CentroidS(:,2),'euclidean');

Answer 1

[Image Analyst]

Try

xy = vertcat(a1RP.Centroid)
distances = pdist2(xy, xy)

Be aware that centroids are x,y, which is (column, row), not (row, column) -- just in case you ever need to do anything with the image itself. plot() should be okay though because it uses x & y.

So you did basically that and got a 100x100 array that gives the distances in pixels between every one of the 100 blobs in your image.

For the spatial calibration, what is 64 microns? What is "pitch"? Is that the distance between pixels, or the full field of view of the image?

If you used XData and YData options in imshow(), then pdist2 should give the output in microns already. If you didn't then the result in in pixels and you'll have to multiply those distances by the spatial calibration factor. Let's say that the pixel to pixel spacing is 64 microns, and you want the distance between the 34th blob and the 78th blob. You can do

dist = distances(34, 78) * 64;

If you want, you can convert the whole distances matrix at once so you don't have to do it one by one:

distances = pdist2(xy, xy) * 64  % ALL spacings will be in microns now.

[darova]

genius as always

♥

[David Mabwa]

Apologies for the delayed response and thank you very much for your help with this.

For the spacial calibration, 64 microns is the distance between an identical point in two neighbouring grid squares. I have attached an image showing what I mean.

The image is a TEM sampling grid, with ~50micron sized grids. I am imaging it in transmission, using a 1.7um laser. I am doing this to see what sort of resolution the particular sensor I am using can achieve, in practice.

I've managed to get the pixel count I wanted, thank you again!

[David Mabwa]

the image I attached was collected using a visible light microscope.

Answer 2

[darova]

pdist2 finds distances between every point (every possible combinations. Zeros in matrix means distance to points themselves)

→ → →

Also you use pdist2 in a wrong way. Has to be:

CentroidDistances=pdist2(CentroidS,CentroidS,'euclidean');
% something like D=pdist2(xy,xy)

Can you just pick two point, calculate distance and count the number of squares between?

[David Mabwa]

Apologies for the delayed response.

Thank you for your suggestions. Is it possible to insert a movable distance line in a plot without saving the plot itself? I have found a way to do so with a function created by another matlab expert, but it seems to rely on saved image data, I can't seem to find a way to place a movable distance tool onto plot data.

In anycase, the distance I seem to get between two centroids is ~17 pixels.

[darova]

What is 'movable distance'? Can you explain or show?

[David Mabwa]

I've attached the an example.

What I mean is a distance tool which changes value (linked to the x and y axis) as you stretch the line or after the line has been stretched to a particular length.

If this is not possible I am not completely worried as there are other ways of doing it, it just seemed like it would be a useful thing to be able to do.

[darova]

Try this

User picks two points, find correspoding points in existing data, calculate distance between them

[David Mabwa]

Wow, thank you very much, that worked exactly the way I had hoped. Thank you!