elimination of consecutive regions

I need to effectively eliminate consecutive regions in vector "a" or better in rows/columns of matrix "A" with length of separate ones regions greater than positive integer N <= length(A):

See following example:

N = 2    % separate consecutive regions with length > 2 are zeroed
a =      [0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1]

a_elim = [0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1]

or 2D case:

N = 2
A =    [1 0 1 …
        1 1 0 …
        1 1 0 …
        0 0 1 …
        1 1 1]

% elimination over columns
A_elim= 0 0 1 
        0 1 0
        0 1 0
        0 0 1
        1 1 1
% elimination over rows
A_elim= 1 0 1 
        1 1 0
        1 1 0
        0 0 1
        0 0 0

I am looking for effective vectorized function performing this task for size(A) ~ [100000, 1000] (over columns case).

Answer 1

[Matt J]

    e=ones(N+1,1); 

if mod(N,2) %even mask

      mask=~conv2(conv2(A,e,'valid')>=N+1 ,[zeros(N,1);e])>0;

      mask=mask(N+1:end,:);

else %odd mask

   mask=~(conv2( conv2(A,e,'same')>=N+1, e,'same')>0);

end

A_elim=A.*mask;

[Bruno Luong]

The above code is not working for N odd (e.g. N=1)

[Matt J]

I've modified it to handle odd N.

[Michal]

Hi Matt … now your solution works very well. Is faster and significantly less memory consuming than Bruno's code. Moreover, the "mask" is very useful to know.

Thanks!!!

Answer 2

[Bruno Luong]

You could use Huffman encoding (there might be some on the FEX), but the idea is similar to this direct code:

N = 2
A = [1 0 1;
     1 1 0;
     1 1 0;
     0 0 1;
     1 1 1];

% Engine for working along the column (1st dimension)
[m,n] = size(A);
z = zeros(1,n);
Apad = [z; A; z];
d = diff(Apad,1,1);
[i1,j1] = find(d==1);
[i0,j0] = find(d==-1);
lgt = i0-i1;
keep1 = lgt <= N;
keep0 = keep1 & i0 <= m;
i1 = [i1,j1];
i0 = [i0,j0];
C1 = accumarray(i1(keep1,:),1,[m n]);
C0 = accumarray(i0(keep0,:),-1,[m n]);
Aclean = cumsum(C1+C0,1);

Aclean

If you want to filter along the 2nd dimension, transpose A, apply the above, then transpose the result Aclean.

[Michal]

Does it mean, that use of Huffman encoding brings some performance improvement?

[Bruno Luong]

It depends how it's implemented. If it's a C-MEX file might be, pure MATLAB Huffman, no chance.

Otherwise my code is probably quite fast (but it creates few big intermediate arrays, you might add "clear...) while the code is running when an array is finished to be used).

Why not test yourself with different methods the link you have found?

[Michal]

Yes, you are right, the pure MATLAB Huffman encoding is not quite fast. I will test all options. Anyway, your code looks as very good method.

Thanks!

Answer 3

[Michal]

good idea (only 1D) is here