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[Matlab] Transform generated table to equation for for loop usage

  1. May 11, 2013 #1
    I have posted a question on here before regarding the generation of a number sequence. I followed up that question with an answer. However, as I have developed my code more I need to use an equation instead of a lookup table.

    Note: I'm using MATLAB

    Given a matrix A of size r x c where r >= 3, c >= 3 I need to map the center point of a 3 x 3 raster segment to a point in A. The raster segments go from left to right, top to bottom. For example, if

    Code (Text):
    A = [0 1 1 0 1 0 1 0 1;...
          0 0 1 0 0 1 1 0 1;...
          1 0 1 1 0 1 0 1 0;...
          1 1 1 1 1 1 1 1 1];...
    The location of (2,2) in each raster segment can be found as follows.

    Code (Text):
    %raster binary image matrix into 3x3 segments
    M = im2col(FP, [3,3],'sliding');

    [ri ci] = size(A);
    [rM cM] = size(M);

    %Generate table of locations in binary image matrix for center point (2,2) of segment matrices
    rownums = repmat([2:ri-1],cM/(ri-2),1);
    rownums = rownums(:);

    colnums = repmat([2:ci-1]',1,cM/(ci-2));
    colnums = colnums(:);

    locations = [rownums,colnums]
    I only need matrix M to find what rM and cM are. Instead of using the im2col() function, I can use the equations below. cM is the number of total raster segments

    Code (Text):
    rM = 9;
    cM = (ci-2)*(ri-2);
    I do some matrix operations for each raster segment using a for loop

    Code (Text):
    n = 1;

    k = 1;
    for row = 1:ri-2
     
        for col = 1:ci-2
     
               %some operations
                   
                    if %condition is met
                        %transform center point location in raster segment
                        %to corresponding location in matrix A
                        Iloc(n,:) = locations(k,:);
                        n = n+1;
                    end
               
                else   %if condition is not met, increment segment counter k and continue
                        %in for loop to next segment
                    k = k+1;
                    continue
                end
            k = k+1;
        end
       
    end
    I would like to replace this line of code
    Code (Text):
    Iloc(n,:) = locations(k,:);
    with equations for the row and column location in A instead of looking up in the table for these locations. The reason for this is that if I have a matrix A of size 274 x 234, I would have 63104 raster segments. This means that my location table matrix would be 63104 x 2. This takes up a lot of memory with the other stuff that I am doing. I know it's possible to come up with some equation that's dependent on the value of row, col, and k. It seems that every (ci-2) kth value, the row in A increments by one. For every different row value, the column values go from 2:(ci-1).
    Question is how do I activate the row increment and column range for every (ci-2) kth value?
     
  2. jcsd
  3. May 11, 2013 #2

    kreil

    User Avatar
    Gold Member

    My first reaction is that instead of summing over rows and columns you can probably vectorize the operation to save a lot of memory. Nested for loops are really expensive here, so it's worth looking in to.

    Also, im2col() puts the 3x3 matrices in the columns of M, so that M(5,:) is the row vector of the (2,2) element in each 3x3 matrix.

    Then

    m = reshape(M(5,:),272,232)

    turns that vector of centers into the same form as it is in A, and is equivalent to A with the edge values shaved off, A(2:end-1,2:end-1).

    Each element in this matrix corresponds to the center of one of the 3x3 matrices, and the indices are each padded by 1, i.e. the (1,1) element in m is the (2,2) element in A, and so on.
     
  4. May 11, 2013 #3
    kreil, within the nested for loops I submit the raster segment to a trained neural network to see if there is a match (part of the project criteria). The simulation of the neural network goes in place of "some operations". If I return a match, then I proceed to get the location from the table that's the if logic statement. Once I get all the locations, I use a logical mask to color a pixel red at transformed locations. There are two ways that I can go about this. The first method I tried was to just use one for loop that cycles through each raster segment in M. This is originally why I needed the table for the locations. The reason why I'm leaning towards the nested for loop is because I don't have to store anything, such as the huge M matrix or the table locations if I can transform the table calculations to equations. Any thoughts on this?

    I've attached the necessary files to run this program. The main program is locateBifurcation. I've included a fingerprint image in case you wanted to test this on a full fingerprint instead of the small test logic matrix I created. The image must first get passed into imread() then into preprocess(I) to convert to a binary matrix.
     

    Attached Files:

    Last edited: May 11, 2013
  5. May 12, 2013 #4
    I think I figure this out. Simple solution actually, don't know why I didn't think of this before. I just replaced the table look up with the row and col value added by one from the for loops.
    Code (Text):

    if %condition is met
       %transform center point location in raster segment
       %to corresponding location in matrix A
       Iloc(n,:) = [row+1,col+1];
       %Iloc(n,:) = locations(k,:);
       n = n+1;
    end
     
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