after minutiae extraction from Ridges end and bifurcation point now how to compute ridges end and bifurcation point and location separately from fingerprint images.....code is bellow to extract minutiae.could anyone help me?

%Minutiae extraction
s=size(thin_image);
N=3;%window size
n=(N-1)/2;
r=s(1)+2*n;
c=s(2)+2*n;
double temp(r,c);   
temp=zeros(r,c);bifurcation=zeros(r,c);ridge=zeros(r,c);
temp((n+1):(end-n),(n+1):(end-n))=thin_image(:,:);
outImg=zeros(r,c,3);%For Display
outImg(:,:,1) = temp .* 255;
outImg(:,:,2) = temp .* 255;
outImg(:,:,3) = temp .* 255;
for x=(n+1+10):(s(1)+n-10)
    for y=(n+1+10):(s(2)+n-10)
        e=1;
        for k=x-n:x+n
            f=1;
            for l=y-n:y+n
                mat(e,f)=temp(k,l);
                f=f+1;
            end
            e=e+1;
        end;
         if(mat(2,2)==0)
            ridge(x,y)=sum(sum(~mat));
            bifurcation(x,y)=sum(sum(~mat));
         end
    end;
end;

% RIDGE END FINDING
[ridge_x ridge_y]=find(ridge==2);
len=length(ridge_x);
%For Display
for i=1:len
    outImg((ridge_x(i)-3):(ridge_x(i)+3),(ridge_y(i)-3),2:3)=0;
    outImg((ridge_x(i)-3):(ridge_x(i)+3),(ridge_y(i)+3),2:3)=0;
    outImg((ridge_x(i)-3),(ridge_y(i)-3):(ridge_y(i)+3),2:3)=0;
    outImg((ridge_x(i)+3),(ridge_y(i)-3):(ridge_y(i)+3),2:3)=0;

      outImg((ridge_x(i)-3):(ridge_x(i)+3),(ridge_y(i)-3),1)=255;
      outImg((ridge_x(i)-3):(ridge_x(i)+3),(ridge_y(i)+3),1)=255;
      outImg((ridge_x(i)-3),(ridge_y(i)-3):(ridge_y(i)+3),1)=255;
      outImg((ridge_x(i)+3),(ridge_y(i)-3):(ridge_y(i)+3),1)=255;
  end

%BIFURCATION FINDING
[bifurcation_x bifurcation_y]=find(bifurcation==4);
len=length(bifurcation_x);
%For Display
for i=1:len
    outImg((bifurcation_x(i)-3):(bifurcation_x(i)+3),(bifurcation_y(i)-3),1:2)=0;
    outImg((bifurcation_x(i)-3):(bifurcation_x(i)+3),(bifurcation_y(i)+3),1:2)=0;
    outImg((bifurcation_x(i)-3),(bifurcation_y(i)-3):(bifurcation_y(i)+3),1:2)=0;
    outImg((bifurcation_x(i)+3),(bifurcation_y(i)-3):(bifurcation_y(i)+3),1:2)=0;

      outImg((bifurcation_x(i)-3):(bifurcation_x(i)+3),(bifurcation_y(i)-3),3)=255;
      outImg((bifurcation_x(i)-3):(bifurcation_x(i)+3),(bifurcation_y(i)+3),3)=255;
      outImg((bifurcation_x(i)-3),(bifurcation_y(i)-3):(bifurcation_y(i)+3),3)=255;
      outImg((bifurcation_x(i)+3),(bifurcation_y(i)-3):(bifurcation_y(i)+3),3)=255;
  end
  figure;imshow(outImg);title('Minutiae');

end

[Walter Roberson]

Duplicated by later https://www.mathworks.com/matlabcentral/answers/346754-ridge-and-bifurcation-point-count-and-location-coding-for-minutiae-matching-behalf-of-bellow-code which has a response.