MATLAB: How to find the start and end points of overlapping intervals in one array

intervalsoverlapping

after extracting the connected components from an image and find the start and end points of each connected components that are in order I want to merge these connected components if they are overlapped so I need to find the start and end points
for examples a is the extreme points of each connected components
a = [ 1.5000 95.5000; 82.5000 150.5000; 141.5000 197.5000; 191.5000 357.5000; 400.5000 438.5000; 415.5000 481.5000; 519.5000 667.5000];
and I need the result to be
1.5000 357.5000 400.5000 481.5000 519.5000 667.5000
I used this code found http://www.mathworks.com/matlabcentral/answers/83061-remove-overlapping-index-ranges-within-a-single-array
b=arrayfun(@(x) a(x,1):a(x,2),1:size(a,1),'un',0); k=1; while k<numel(b) c=b(k+1:end); idx=cellfun(@(x) any(ismember(x,b{k})),c); if any(idx) b(logical([ zeros(1,numel(b)-numel(idx)-1) 1 idx]))=[]; else b(logical([ zeros(1,numel(b)-numel(idx)) idx]))=[]; end k=k+1; end out=cell2mat(cellfun(@(x) [x(1) x(end)],b','un',0))
but I got this overlapped points
 141.5000  197.5000
  191.5000  357.5000
  519.5000  667.5000
how can I fix it ?
thanks

Best Answer

a = [ 1.5000 95.5000; 82.5000 150.5000; 141.5000 197.5000; 191.5000 357.5000; 400.5000 438.5000; 415.5000 481.5000; 519.5000 667.5000];
b =  reshape(a',1,[]);
ii = strfind(sign(diff(b)),[-1 1]);
out = b;
out([ii,ii+1]) = [];
add
b =  reshape(a',1,[]);
x = all(tril(bsxfun(@lt,b(:),b(:)'))==0,2);
i0 = strfind(x(:)',[1 0]);
x(i0) = false;
out = b(x);
add2
a = [ 4.5000   58.5000
    4.5000   58.5000
   65.5000  118.5000
   65.5000  118.5000
  140.5000  277.5000
  140.5000  277.5000
  206.5000  223.5000
  206.5000  223.5000
  284.5000  295.5000
  284.5000  295.5000
  360.5000  422.5000
  360.5000  422.5000
  449.5000  454.5000
  449.5000  454.5000
  449.5000  532.5000
  449.5000  532.5000
  532.5000  574.5000
  532.5000  574.5000]
a1 = unique(a,'rows');
out = a1(1,:);
for jj = 2:size(a1,1)
    if out(end,2) > a1(jj,1) && a1(jj,2) > out(end,2)
        out(end,:) = [out(end,1) a1(jj,2)];
    elseif out(end,2) <= a1(jj,1)
        out(end + 1,:) = a1(jj,:);
    end
end
or
a1 = unique(a,'rows');
for jj = 2:size(a1,1)
    if a1(jj-1,2) > a1(jj,1) && a1(jj,2) > a1(jj-1,2)
        a1(jj,1) = 0 ;
        a1(jj-1,2) = 0;
    elseif a1(jj-1,2) >= a1(jj,2)
        a1(jj,:) = 0;
    end
end
out = a1';
out = reshape(out(out>0),2,[])';
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