{"id":231,"date":"2008-10-15T13:16:25","date_gmt":"2008-10-15T17:16:25","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/2008\/10\/15\/dilation-algorithms-performance-of-decomposed-strels\/"},"modified":"2019-10-28T09:45:03","modified_gmt":"2019-10-28T13:45:03","slug":"dilation-algorithms-performance-of-decomposed-strels","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2008\/10\/15\/dilation-algorithms-performance-of-decomposed-strels\/","title":{"rendered":"Dilation algorithms – performance of decomposed strels"},"content":{"rendered":"
\r\n

We looked at the decomposition of different structuring element shapes in my previous post<\/a> on dilation algorithms. Today let's time some code to how decomposition makes a real difference in performance.\r\n <\/p>\r\n

Note that running the code in this post requires that you download my timeit function from the MATLAB Central File Exchange.<\/i><\/p>\r\n

For our test image, I'll use a grayscale version of the peppers image that ships with the Image Processing Toolbox.<\/p>

I = rgb2gray(imread('peppers.png'<\/span>));\r\nimshow(I)<\/pre> 
Let's time dilations of I<\/tt> with disk structuring elements of varying radii. As I mentioned previously, strel('disk',r)<\/tt> creates a structuring element that is a decomposable approximation to a disk.\r\n   <\/p>
% Dilate using radii of 3 through 25.<\/span>\r\nrr1 = 3:25;\r\n\r\n% Initialize the vector that will hold the measured times.<\/span>\r\nt1 = [];\r\nfor<\/span> r = rr1\r\n   se = strel('disk'<\/span>, r);\r\n\r\n   % Make a function that dilates I by the structuring element se.<\/span>\r\n   f = @() imdilate(I, se);\r\n\r\n   % Measure how long the dilation takes.<\/span>\r\n   t1(end + 1) = timeit(f);\r\nend<\/span>\r\n\r\nplot(rr1, t1)\r\ngrid on<\/span>\r\nylabel('Time (seconds)'<\/span>)\r\nxlabel('Disk radius'<\/span>)\r\n% Make sure we show the time scale down to 0.  (Thanks, Chris!)<\/span>\r\nylim([0 max(t1)]);\r\ntitle('Time to compute dilation with decomposable disk'<\/span>)<\/pre> 
Now let's repeat the timing experiment using nondecomposable disks.  You make such a structuring element using the syntax\r\n      strel('disk',r,0)<\/tt>.\r\n   <\/p>\r\n   
(In my first draft of this post, I tried to do this step using the same range of radius values as above, 3-25.  But I got\r\n      tired of waiting for it to finish!)\r\n   <\/p>
% Dilate using radius values 3-8.<\/span>\r\nrr2 = 3:8;\r\nt2 = [];\r\nfor<\/span> r = rr2\r\n   se = strel('disk'<\/span>, r, 0);\r\n   t2(end + 1) = timeit(@() imdilate(I, se));\r\nend<\/span>\r\n\r\n% Plot the results of both experiments together.<\/span>\r\nplot(rr, t1, rr2, t2)\r\ngrid on<\/span>\r\nylabel('Time (seconds)'<\/span>)\r\nxlabel('Disk radius'<\/span>)\r\n% Make sure we show the time scale down to 0.  (Thanks, Chris!)<\/span>\r\nylim([0 max([t1, t2])]);\r\nlegend('Decomposable'<\/span>, 'Nondecomposable'<\/span>);\r\ntitle('Speed comparison: Decomposable vs. Nondecomposable disks'<\/span>)<\/pre> 
I think you can see from the plot above why we chose to use the decomposable disk approximation as the default!<\/p>\r\n   
So what does it look like when you dilate gray peppers with a disk?<\/p>
J = imdilate(I, strel('disk'<\/span>, 25));\r\nimshow(J)<\/pre> 
The resulting blobs look kind of octagony.  That's because of the default decomposition used.  You can ask strel<\/tt> to use a closer approximation to a disk.  It will take a bit longer to compute, although still not nearly as long as using\r\n      the nondecomposable disk.\r\n   <\/p>
se8 = strel('disk'<\/span>, 25, 8);\r\nJ8 = imdilate(I, se8);\r\nimshow(J8)<\/pre> 
Bon appetit!<\/p>