how to find the start and end points of overlapping intervals in one array

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

[Amani]

and I need the result to be

1.5000 357.5000

400.5000 481.5000

519.5000 667.5000

Answer 1

[Andrei Bobrov]

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,[])';

[Amani]

thank you very much

I tried it with these points

 a = 3.5000 86.5000; 3.5000 86.5000; 111.5000 147.5000; 111.5000 147.5000; 148.5000 155.5000; 148.5000 155.5000; 192.5000 245.5000; 192.5000 245.5000; 237.5000 393.5000; 237.5000 393.5000; 259.5000 285.5000; 259.5000 285.5000; 336.5000 349.5000; 336.5000 349.5000; 376.5000 393.5000; 376.5000 393.5000 ]

but I got many overlaps the answer should be

 3.5000   86.5000  111.5000  147.5000  148.5000  155.5000  192.5000  393.5000

but I got this

3.5000   86.5000  111.5000  147.5000  148.5000  155.5000  192.5000  285.5000  336.5000 349.5000  376.5000  393.5000

[Andrei Bobrov]

see after word 'add'

[Amani]

I got some overlaps with these points

a= 2.5000 88.5000; 2.5000 88.5000; 128.5000 198.5000; 128.5000 198.5000; 242.5000 276.5000; 242.5000 276.5000; 248.5000 266.5000; 248.5000 266.5000; 303.5000 459.5000; 303.5000 459.5000; 353.5000 375.5000; 353.5000 375.5000; 495.5000 559.5000; 495.5000 559.5000; 536.5000 559.5000; 536.5000 559.5000; 583.5000 639.5000; 583.5000 639.5000; 668.5000 682.5000; 668.5000 682.5000]

the answer should be

2.5000 88.5000 128.5000 198.5000 242.5000 276.5000 303.5000 459.5000 495.5000 559.5000 583.5000 639.5000 668.5000 682.5000

but I got

 2.5000   88.5000  128.5000  198.5000  242.5000  303.5000  495.5000  559.5000  583.5000  639.5000  668.5000  682.5000

[Amani]

the same problem with these points 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]

it gives me the start points as end points which mix up all the rest of the points

I got this answer

   4.5000   58.5000   65.5000  118.5000  140.5000  284.5000  295.5000  360.5000  422.5000  449.5000  532.5000  532.5000  574.5000

but the answer should be

4.5000 58.5000 65.5000 118.5000 140.5000 295.5000 360.5000 532.5000 532.5000 574.5000

[Amani]

I don't fully understand your algorithm, can you please explain it ?

[Andrei Bobrov]

new code after 'add2'

[Amani]

thank you very much