Vectorizing a nested for loop which fills a dynamic programming table

I was wondering if there was a way to vectorize the nested for loop in this function which is filling up the entries of the 2D dynamic programming table DP. I believe that at the very least the inner loop could be vectorized as each row only depends on the previous row. I'm not sure how to do it though. Note this function is called on large 2D arrays (images) so the nested for loop really doesn't cut it.

    function [cols] = compute_seam(energy)
        [r, c, ~] = size(energy);

        cols = zeros(r);

        DP = padarray(energy, [0, 1], Inf);    
        BP = zeros(r, c);

        for i = 2 : r        
            for j = 1 : c
                [x, l] = min([DP(i - 1, j), DP(i - 1, j + 1), DP(i - 1, j + 2)]);
                DP(i, j + 1) = DP(i, j + 1) + x;
                BP(i, j) = j + (l - 2);
            end
        end

        [~, j] = min(DP(r, :));
        j = j - 1;

        for i = r : -1 : 1
            cols(i) = j;
            j = BP(i, j);
        end
    end