Answer by Jim Gray for Representing and solving a maze given an image

Tree search is too much. The maze is inherently separable along the solution path(s).

(Thanks to rainman002 from Reddit for pointing this out to me.)

Because of this, you can quickly use connected components to identify the connected sections of maze wall. This iterates over the pixels twice.

If you want to turn that into a nice diagram of the solution path(s), you can then use binary operations with structuring elements to fill in the "dead end" pathways for each connected region.

Demo code for MATLAB follows. It could use tweaking to clean up the result better, make it more generalizable, and make it run faster. (Sometime when it's not 2:30 AM.)

% read in and invert the image
im = 255 - imread('maze.jpg');

% sharpen it to address small fuzzy channels
% threshold to binary 15%
% run connected components
result = bwlabel(im2bw(imfilter(im,fspecial('unsharp')),0.15));

% purge small components (e.g. letters)
for i = 1:max(reshape(result,1,1002*800))
    [count,~] = size(find(result==i));
    if count < 500
        result(result==i) = 0;
    end
end

% close dead-end channels
closed = zeros(1002,800);
for i = 1:max(reshape(result,1,1002*800))
    k = zeros(1002,800);
    k(result==i) = 1; k = imclose(k,strel('square',8));
    closed(k==1) = i;
end

% do output
out = 255 - im;
for x = 1:1002
    for y = 1:800
        if closed(x,y) == 0
            out(x,y,:) = 0;
        end
    end
end
imshow(out);

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