Remove centroid locations of objects that are too close

Hi, I have a list of centroid locations of spots in an image (xf, yf). The spots are randomly distributed. I want to remove the centroid locations that are too close to each other, or say within a distance of d. I've got to the following but not sure what to do next. Also is there a better way to do this ratrher than use loops?

%using a loop
M=[];
for j=1:length(xf)
    for i=1:length(xf)
        dx=xf(j)-xf(i);
        dy=yf(j)-yf(i);
        dr=sqrt(power(dx,2)+power(dy,2));
        M(j,1)=xf(j);
        M(j,2)=yf(j);
        M(j,3)=xf(i);
        M(j,4)=yf(i);
        M(j,5)=dr;    
    end    
end

[Matt J]

If two spots are less than d apart should both be removed? If not, by what criterion do you decide which spot remains?

[Image Analyst]

To me it sounds like both are to be removed. This is easily done with pdist2.

Answer 1

[Matt J]

A=[xf(:) yf(:)];
D=pdist2(A,A);
D(D==0)=inf; %retroactive EDIT

keep = all(D>d,1);

xf=xf(keep);
yf=yf(keep);

[Jason]

Thankyou Matt. Its almost there. Its not removing the 2nd centroid of the "close pair" of objects.

I've set the cut of distance to be 40.

A and D from your code gives this:

A =

15.88         18.43
33.48         14.99
53.49         37.71


D =

0         17.94         42.27
17.94             0         30.27
42.27         30.27             0

This is my Matrix where col 1,2 are centroids of each spot, col 3,4 are then centroid of all other spots, col 5 is the distance between all pairs of spots.:

M =

15.88         18.43         15.88         18.43             0
15.88         18.43         33.48         14.99         17.94
15.88         18.43         53.49         37.71         42.27
33.48         14.99         15.88         18.43         17.94
33.48         14.99         33.48         14.99             0
33.48         14.99         53.49         37.71         30.27
53.49         37.71         15.88         18.43         42.27
53.49         37.71         33.48         14.99         30.27
53.49         37.71         53.49         37.71             0

[Matt J]

Make sure you are using my most updated version. Your D matrix should have NaNs along the diagonal. Not zeros.

[Matt J]

I see now that D should have Infs along the diagonals, not NaNs, but even so with d=40, none of your objects are sufficiently remote, so all centroids get removed. With d=30, one blob remains.

A =[
15.88         18.43
33.48         14.99
53.49         37.71]; d=30;

D=pdist2(A,A);
D(D==0)=Inf

D = 3×3

Inf 17.9330 42.2638 17.9330 Inf 30.2754 42.2638 30.2754 Inf

keep = all(D>d,1)

keep = 1×3 logical array
   0   0   1

A=A(keep,:)

A = 1×2

53.4900 37.7100

[Jason]

Perfect, thanks. Can you explain the bit about replacing the Nan with Inf, I don't follow this part.

Thanks

Jason

[Matt J]

We don't want to consider the distance between an object and itself, so we need to set the diagonal of D to something that will automatically satisfy the distance cut-off criterion.

[Jason]

Of course, its clear now, thankyou

[Jason]

Just to add, when I had over 400 objects, akthough i do other operations, using the for loop took 110s.using the pdist2 approach took just under 2s. Remarkable!

Answer 2

[yanqi liu]

yes，sir，may be use pdist2， such as

xf = rand(1, 10);
yf = rand(1, 10);
%using a loop
M=[];
for j=1:length(xf)
    for i=1:length(xf)
        dx=xf(j)-xf(i);
        dy=yf(j)-yf(i);
        dr=sqrt(power(dx,2)+power(dy,2));
        M(end+1,1)=xf(j);
        M(end,2)=yf(j);
        M(end,3)=xf(i);
        M(end,4)=yf(i);
        M(end,5)=dr;
    end
end
% second method
A=[xf(:) yf(:)];
B=pdist2(A,A);
C=B';
C=C(:);
isequal(M(:,end),C)

ans = logical
   1