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

[roldy]

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

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.

%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

rM = 9;
cM = (ci-2)*(ri-2);

I do some matrix operations for each raster segment using a for loop

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

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?

 

[kreil]

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.

 

[roldy]

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.

 

[roldy]

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.

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