create matrix in which for every element of matrix B found closest element of matrix A

Question

So I can't find simple way of solving following problem: I've got two matrices with same amount of rows:

A = [547   184   929   306;
     296   368   776   509;
     745   626   487   511;
     189   780   436   818;
     687    81   447   795]
B = [644   939   208   195   311   980;
     379   876   301   226   923   439;
     812   550   471   171   430   111;
     533   622   230   228   185   258;
     351   587   844   436   905   409]

How can I create matrix C (size(C)=size(B)) in which for every element of matrix B found closest element of matrix A from corresponding row. In current case:

C =

   547   929   184   184   306   929
   368   776   296   296   776   509
   745   511   487   487   487   487
   436   780   189   189   189   189
   447   687   795   447   795   447  

For the moment I've only thought of this:

temp = bsxfun(@eq,abs(bsxfun(@minus,repmat(A,1,1,size(B,2)),permute(B,[1,3,2]))),min(abs(bsxfun(@minus,repmat(A,1,1,size(B,2)),permute(B,[1,3,2]))),[],2));

C = permute(sum(temp.*repmat(A,1,1,size(B,2)),2),[1,3,2]);

So is there any easy and more understandable way to solve this task?

Answer 1

The three bsxfun can be reduced to one by using the second output of min, which gives the position of the minimum (first line of my code). Those positions are then converted to a linear index, which is applied to A (second line):

[~, jj] = min(abs(bsxfun(@minus, permute(A, [1 3 2]), B)), [], 3);
C = A(sub2ind(size(B), ndgrid(1:size(B,1),1:size(B,2)), jj));

Answer 2

You can also do it using nearest neighbour interpolation:

for row = 1:size(A,1)
  I = interp1(A(row,:), 1:size(A,2), B(row,:), 'nearest','extrap');
  C(row,:)=A(row,I);
end