{"id":36,"date":"2006-02-21T07:00:52","date_gmt":"2006-02-21T12:00:52","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=36"},"modified":"2021-06-17T10:32:57","modified_gmt":"2021-06-17T14:32:57","slug":"tracing-george","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2006\/02\/21\/tracing-george\/","title":{"rendered":"Tracing George"},"content":{"rendered":"
\r\n<\/span>\r\n

Note<\/strong><\/p>\r\n

See the 17-Jun-2021 post<\/a> for new or updated information about this topic.<\/p>\r\n<\/div>\r\n\r\n

\r\n

Last time<\/a>, in my spatial transformations series, I introduced the head-and-shoulders outline that I like to call George (George\r\n P. Burdell). Today I want to diverge briefly from my main topic and show how I recently \"recovered\" George.\r\n <\/p>\r\n

George appears in section 5.11 of Digital Image Processing Using MATLAB. While working on the book, I tried to keep all data\r\n files and M-files necessary for regenerating the book's figures. I found, however, that I could not locate the data for George's\r\n curve that appears in Figure 5.12 and Table 5.3.\r\n <\/p>\r\n

After a few minutes of head scratching, I decided to get the curve data by taking a digital snapshot of the figure in the\r\n book. Here's a cropped version:\r\n <\/p>

url = 'https:\/\/blogs.mathworks.com\/images\/steve\/36\/george.jpg'<\/span>;\r\nI = imread(url);\r\nimshow(I)<\/pre> 
A little fuzzy and dark, but maybe workable.  The first step is to threshold the image.  The Image Processing Toolbox function\r\n      graythresh<\/tt> computes binarization thresholds automatically.  It works well for a variety of images.\r\n   <\/p>
threshold = graythresh(I);\r\nbw = im2bw(I, threshold);\r\nimshow(bw)<\/pre> 
Now we have a nice fat line.  Toolbox function bwmorph<\/tt> has a thinning option, but it works on white (foreground) pixels instead of black pixels.  So complement the image:\r\n   <\/p>
bw2 = ~bw;<\/pre>
and then thin it.  Specify the number of iterations to be Inf<\/tt> so that bwmorph<\/tt> will keep thinning until the lines are a single pixel wide.\r\n   <\/p>
bw3 = bwmorph(bw2, 'thin'<\/span>, inf);\r\nimshow(bw3)<\/pre> 
Now trace the line using toolbox function bwboundaries<\/tt>.\r\n   <\/p>
boundaries = bwboundaries(bw3);<\/pre>
boundaries<\/tt> is a cell array containing one P-by-2 matrix for each object boundary.  This image contains only one object, so boundaries<\/tt> contains only one P-by-2 matrix.  The matrix has twice as many rows as we need, because bwboundaries<\/tt> traces all the way around the object.\r\n   <\/p>
b = boundaries{1};\r\nb = b(1:floor(end\/2), :);<\/pre>
Finally we are ready to plot the curve.<\/p>
x = b(:,2);\r\ny = b(:,1);\r\nplot(x,y)\r\naxis ij<\/span>     % Place the origin at upper left, with y values increasing from<\/span>\r\n            % top to bottom.<\/span>\r\naxis equal<\/span>  % Set the aspect ratio so that the data units are the same in<\/span>\r\n            % every direction.<\/span>\r\ntitle('George P. Burdell'<\/span>)<\/pre>