{"id":246,"date":"2009-01-28T18:05:02","date_gmt":"2009-01-28T23:05:02","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/2009\/01\/28\/have-you-heard-of-the-feature-transform\/"},"modified":"2019-10-28T15:24:56","modified_gmt":"2019-10-28T19:24:56","slug":"have-you-heard-of-the-feature-transform","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2009\/01\/28\/have-you-heard-of-the-feature-transform\/","title":{"rendered":"Have you heard of the “feature transform”?"},"content":{"rendered":"
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Today I want to know if you've heard of an operation sometimes called the feature transform<\/i>, and whether you've had a particular application for it.\r\n <\/p>\r\n

But first, greetings to those who attended the SPIE Electronic Imaging Conference in California last week. I heard yesterday\r\n that several people who stopped at the MathWorks booth mentioned the blog. Sorry I missed you! Your feedback has motivated\r\n me to get back to the keyboard and put up some new posts.\r\n <\/p>\r\n

Now about the feature transform. I've been thinking about this operation because we've been having some design discussions\r\n recently about an Image Processing Toolbox function called bwdist<\/tt>, which computes the Euclidean distance transform. For each pixel in a binary image, bwdist<\/tt> computes the distance between that pixel and the nearest foreground (nonzero) pixel.\r\n <\/p>\r\n

Here's a small example to show you what I mean.<\/p>

bw = magic(5) > 21<\/pre>
\r\nbw =\r\n\r\n     0     1     0     0     0\r\n     1     0     0     0     0\r\n     0     0     0     0     1\r\n     0     0     0     0     0\r\n     0     0     1     0     0\r\n\r\n<\/pre>
D = bwdist(bw)<\/pre>
\r\nD =\r\n\r\n    1.0000         0    1.0000    2.0000    2.0000\r\n         0    1.0000    1.4142    1.4142    1.0000\r\n    1.0000    1.4142    2.0000    1.0000         0\r\n    2.0000    1.4142    1.0000    1.4142    1.0000\r\n    2.0000    1.0000         0    1.0000    2.0000\r\n\r\n<\/pre>
And here's a bigger example, where I display the distance transform as a false-color image.<\/p>
bw2 = false(400, 400);\r\nbw2(200, 200) = true;\r\nbw2(100, 100:300) = true;\r\nbw2(300, 100:300) = true;\r\nbw2(100:300, 100) = true;\r\nbw2(100:300, 300) = true;\r\nimshow(bw2)<\/pre> 
D2 = bwdist(bw2);\r\nimshow(D2, [])\r\ncolormap(copper)<\/pre> 
It seems that not many people (even at MathWorks!) know that bwdist<\/tt> has an optional second output that tells you, for each image pixel, which<\/b> foreground pixel it is closest to.  This is the thing that's sometimes called the feature transform<\/i>, or closest feature transform.<\/i> The second output is a matrix of linear indices.  (See my linear indexing post<\/a>.)  Here's what it looks like for the small matrix I started with.\r\n   <\/p>
bw<\/pre>
\r\nbw =\r\n\r\n     0     1     0     0     0\r\n     1     0     0     0     0\r\n     0     0     0     0     1\r\n     0     0     0     0     0\r\n     0     0     1     0     0\r\n\r\n<\/pre>
[D, L] = bwdist(bw);\r\nL<\/pre>
\r\nL =\r\n\r\n     2     6     6     6    23\r\n     2     6     6    23    23\r\n     2     2    15    23    23\r\n     2    15    15    15    23\r\n    15    15    15    15    23\r\n\r\n<\/pre>
Looking at L<\/tt> tells us that the pixel with linear index 2 (2nd row, 1st column) is the closest foreground pixel to 5 image pixels, including\r\n      itself. (Ties are broken in some arbitrary fashion.)\r\n   <\/p>\r\n   
I've come across one user application for this capability: a 3-D blood vessel tracing algorithm that I mentioned in this old post from 2006<\/a>.\r\n   <\/p>\r\n   
Do you have an application for the feature transform?  Let us know by commenting<\/a>.<\/p>