Question

I am trying to implement my own Thinning Algorithm in Matlab to understand the thinning algorithm. I am following http://fourier.eng.hmc.edu/e161/lectures/morphology/node2.html and implementing my own code, but the result is incorrect.

Here is my code:

%for the sake of simplicity, the outermost pixels are ignored.
for x = 2:1:511
    for y = 2:1:511

        % if this pixel is not black, then, proceed in.
        if (frame2(y,x) > 0)                

            % the pos(1 to 8) here are for the surrounding pixels.
            pos(1) = frame2(y-1,x-1);
            pos(2) = frame2(y, x-1);
            pos(3) = frame2(y+1, x+1);
            pos(4) = frame2(y+1, x);
            pos(5) = frame2(y+1, x-1);
            pos(6) = frame2(y, x-1);
            pos(7) = frame2(y-1, x-1);
            pos(8) = frame2(y-1, x);

            nonZeroNeighbor = 0;
            transitSequence = 0;
            change = 0;

            for n = 1:1:8
                % for N(P1)
                if (pos(n) >= 1)
                    nonZeroNeighbor = nonZeroNeighbor + 1;
                end

                % for S(P1)
                if (n > 1)
                    if (pos(n) ~= change)
                        change = pos(n);
                        transitSequence = transitSequence + 1;
                    end
                else
                    change = pos(n);
                end

            end

            % also for S(P1)
            if ((nonZeroNeighbor > 1 && nonZeroNeighbor < 7) || transitSequence >= 2)
                markMatrix(y,x) = 1;
                fprintf(1, '(%d,%d) nonzero: %d transit: %d\n', y,x, nonZeroNeighbor, transitSequence);
            else %this else here is for the reverse.

            end

        end
    end
end


    for x = 2:1:511
        for y = 2:1:511
            if (markMatrix(y,x) > 0)
                frame2(y,x) = 0;
            end
        end
    end

    savePath = [path header number2 '.bmp']; 

    imwrite(frame2, savePath, 'bmp'); %output image here, replacing the original

From the site above, it states the function S(P1) as:

“S(P1): number of 0 to 1 (or 1 to 0) transitions in the sequence (P2, P3, …, P9)”

For this part, my codes are below “% for S(P1)” and “% also for S(P1)” comments. Am I implementing this function correctly? The output image I got is simply blank. Nothing at all.

For the correct output, I am aware that there is a logical problem. Regarding the site, it states:

When part of the shape is only 2-pixel wide, all pixels are boundary points and will be marked and then deleted.

This problem is to be ignored for now.

Answer 1

I’ve had a go at the problem and think I managed to get the algorithm to work. I’ve made several small edits along the way (please see the code below for details), but also found two fundamental problems with your initial implementation.

Firstly, you assumed all would be done in the first pass of step 1 and 2, but really you need to let the algorithm work away at the image for some time. This is typical for iterative morphological steps ‘eating’ away at the image. This is the reason for the added while loop.

Secondly, your way of calculating S() was wrong; it counted both steps from 0 to 1 and 1 to 0, counting twice when it shouldn’t and it didn’t take care of the symmetry around P(2) and P(9).

My code:

%Preliminary setups
close all; clear all;
set(0,'DefaultFigureWindowStyle','Docked')

%Read image
frame2 = imread('q1.jpg');

%Code for spesific images
%frame2(:,200:end) = [];
%frame2 = rgb2gray(frame2);

%Make binary
frame2(frame2 < 128) = 1;
frame2(frame2 >= 128) = 0;

%Get sizes and set up mark
[Yn Xn] = size(frame2);
markMatrix = zeros(Yn,Xn);

%First visualization
figure();imagesc(frame2);colormap(gray)
%%

%While loop control
cc = 0; 
changed = 1;
while changed && cc < 50;

    changed = 0;
    cc = cc + 1;
    markMatrix = zeros(Yn,Xn);

    for x = 2:1:Xn-1
        for y = 2:1:Yn-1

            % if this pixel is not black, then, proceed in.
            if (frame2(y,x) > 0)                

                % the pos(2 to 9) here are for the surrounding pixels.
                pos(1) = frame2(y,   x);
                pos(2) = frame2(y-1, x);
                pos(3) = frame2(y-1, x+1);
                pos(4) = frame2(y,   x+1);
                pos(5) = frame2(y+1, x+1);
                pos(6) = frame2(y+1, x);
                pos(7) = frame2(y+1, x-1);
                pos(8) = frame2(y,   x-1);
                pos(9) = frame2(y-1, x-1);

                nonZeroNeighbor = 0;
                transitSequence = 0;
                change = pos(9);

                for n = 2:1:9

                    %N()
                    nonZeroNeighbor = sum(pos(2:end));

                    %S()
                    if (double(pos(n)) - double(change)) < 0
                        transitSequence = transitSequence + 1;
                    end
                    change = pos(n);

                end

                %Test if pixel is to be removed
                if ~( nonZeroNeighbor == 0 || nonZeroNeighbor == 1 ...
                    ||nonZeroNeighbor == 7 || nonZeroNeighbor == 8 ...
                    ||transitSequence >= 2)

                        markMatrix(y,x) = 1;
                        fprintf(1, '(%d,%d) nonzero: %d transit: %d\n', ...
                            y,x, nonZeroNeighbor, transitSequence);
                end

            end
        end
    end

    %Mask out all pixels found to be deleted
    frame2(markMatrix > 0) = 0;

    %Check if anything has changed
    if sum(markMatrix(:)) > 0;changed = 1;end

end

%Final visualization
figure();imagesc(frame2);colormap(gray)