How to vectorize the following for...loop?

Dear colleagues,

I have written the following MATLAB code, with two for...loops, which compute the distance map of an image. However, the code is relatively slower, and I want to speed it up using vectorization techniques. I am still a newbie in code optimization; still learning. Any idea on how to vectorize the code, please share:

function [ res ] = computeDT( v, d1, d2 )
%%COMPUTEDT -- Compute the distance field of an input image, img
%  v   -- Input image
%  res -- Output image
%%%%%%%Initialize the input image
v = v([1,1:end,end],[1,1:end,end]); 
v(v~=0) = inf;
% Weights [0 +d1 +d2]
%%Forward pass

M1 = size(v,2); % Number of columns
M2 = size(v,1); % Number of lines (rows)
for k1=2:M1-1
    for k2=2:M2-1
        v(k1,k2) = min([v(k1 - 1, k2 - 1) + d2, v(k1 - 1, k2) + d1,... 
                        v(k1 - 1, k2 + 1) + d2, v(k1, k2 - 1) + d1, v(k1, k2)]);
    end
end
%%Backward pass

for k1=M1-1:-1:2
    for k2=M2-1:-1:2
        v(k1,k2) = min([v(k1, k2), v(k1, k2 + 1) + d1, v(k1 + 1, k2 - 1) + d2,...
                       v(k1 + 1, k2) + d1, v(k1 + 1, k2 + 1) + d2]);
    end
end
res = v(2:end-1,2:end-1);
% save res.mat
% subimage(mat2gray(res))
end

[Kuifeng]

can you give an example value/matrix of v, d1, d2?

Answer 1

[Kuifeng]

% maybe make some changes to the following code could help,

 [rows cols] = size(ans);
v1 = v(1:rows-1, 1:cols-1);
v2 = v(2:rows, 1:cols-1);
v3 = v(1:rows-1, 2:cols);
v4 = v(2:rows, 2:cols);
result = min[v1+d1, v2+d2, v3, v4, v5]; %for example only, revise accordingly

[Baraka Maiseli]

Thank you Kuifeng for the response. I am trying to make the code snippet above working. I have embedded it in the original code, and did a little modifications to suit my needs, but still the results are not the ones I expect. Considering just the "Forward pass" (please see comments in the original code), I have adopted your recommendation as follows:

result = min([v1(1:rows - 2, 1:cols - 2) + d2, v1(1:rows - 2, 2:cols - 1) + d1, v1(1:rows - 2, 3:cols) + d2, v1(2:rows - 1, 1:cols - 2) + d1, v1(2:rows - 1, 2:cols - 1)]);

But, this provides a wrong answer. I still don't understand where the mistakes are.

[Kuifeng]

 %for example in the 'forward pass', 
  [rows cols] = size(v);
v1 = v(1:rows-2, 1:cols-2);
v2 = v(1:rows-2, 2:cols-1);
v3 = v(1:rows-2, 3:cols);
v4 = v(2:rows-1, 1:cols-2);
v5 = v(2:rows-1, 2:cols-1);
result = min(min(min(min(v1 + d2, ...
    v2 + d1), ...
    v3 + d2), ...
    v4 + d1), ...
    v5);

[Baraka Maiseli]

Testing the code snippet (for the forward pass), as it is, I get:

     Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf     0     1   Inf   Inf
     Inf   Inf   Inf     1   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf

But the old code, which I use as reference, gives:

     Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf
     Inf   Inf   Inf   Inf     0     1     2     3   Inf
     Inf   Inf   Inf   Inf     1     2     3     4   Inf
     Inf   Inf   Inf   Inf     2     3     4     5   Inf
     Inf   Inf   Inf   Inf     3     4     5     6   Inf
     Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf   Inf

The two implementations produce different results.