{"id":2511,"date":"2017-03-07T16:01:06","date_gmt":"2017-03-07T21:01:06","guid":{"rendered":"https:\/\/blogs.mathworks.com\/steve\/?p=2511"},"modified":"2019-11-01T17:05:45","modified_gmt":"2019-11-01T21:05:45","slug":"logical-indexing-2","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/steve\/2017\/03\/07\/logical-indexing-2\/","title":{"rendered":"Logical indexing"},"content":{"rendered":"

One of my favorite aspects of MATLAB for image processing is how I can use a binary image to index directly into a grayscale image. The technique is called logical indexing<\/i>, and I'm going to show you how it works today.<\/p>

Note: this is an update of a post I originally wrote in 2008<\/a><\/i>.<\/p>

Let me start with a small example. (As regular readers know, I like to use magic squares for small matrix examples.)<\/p>

A = magic(5)\r\n<\/pre>
\r\nA =\r\n\r\n    17    24     1     8    15\r\n    23     5     7    14    16\r\n     4     6    13    20    22\r\n    10    12    19    21     3\r\n    11    18    25     2     9\r\n\r\n<\/pre>
Every MATLAB user is familiar with ordinary matrix indexing notation.<\/p>
A(2,3)\r\n<\/pre>
\r\nans =\r\n\r\n     7\r\n\r\n<\/pre>
A(2,3)<\/tt> extracts the 2nd row, 3rd column of the matrix A<\/tt>. You can extract more than one row and column at the same time:<\/p>
A(2:4, 3:5)\r\n<\/pre>
\r\nans =\r\n\r\n     7    14    16\r\n    13    20    22\r\n    19    21     3\r\n\r\n<\/pre>
When an indexing expression appears on the left-hand side of the equals sign, that's an assigment. You are changing one or more of the values of the variable on the left-hand side.<\/p>
A(5,5) = 100\r\n<\/pre>
\r\nA =\r\n\r\n    17    24     1     8    15\r\n    23     5     7    14    16\r\n     4     6    13    20    22\r\n    10    12    19    21     3\r\n    11    18    25     2   100\r\n\r\n<\/pre>
Here is a frequently-asked MATLAB question: How do I replace all the NaNs in my matrix B with 0s?<\/i><\/p>
An experienced MATLAB user will immediately answer:<\/p>
B(isnan(B)) = 0;<\/pre>
For example:<\/p>
B = rand(3,3);\r\nB(2, 2:3) = NaN\r\n<\/pre>
\r\nB =\r\n\r\n    0.2217    0.3188    0.0855\r\n    0.1174       NaN       NaN\r\n    0.2967    0.5079    0.8010\r\n\r\n<\/pre>
Replace the NaNs with zeros:<\/p>
B(isnan(B)) = 0\r\n<\/pre>
\r\nB =\r\n\r\n    0.2217    0.3188    0.0855\r\n    0.1174         0         0\r\n    0.2967    0.5079    0.8010\r\n\r\n<\/pre>
The expression B(isnan(B))<\/tt> is an example of logical indexing<\/i>. Logical indexing is a compact and expressive notation that's very useful for many image processing operations.<\/p>
Let's talk about the basic rules of logical indexing, and then we'll reexamine the expression B(isnan(B))<\/tt>.<\/p>
If C<\/tt> and D<\/tt> are matrices, then C(D)<\/tt> is a logical indexing expression if D<\/tt> is a logical<\/i> matrix.<\/p>
Logical<\/i> is one of the fundamental data types for MATLAB arrays. Relational operators, such as ==<\/tt> or ><\/tt>, produce logical arrays automatically.<\/p>
C = hilb(4)\r\n<\/pre>
\r\nC =\r\n\r\n    1.0000    0.5000    0.3333    0.2500\r\n    0.5000    0.3333    0.2500    0.2000\r\n    0.3333    0.2500    0.2000    0.1667\r\n    0.2500    0.2000    0.1667    0.1429\r\n\r\n<\/pre>
D = C > 0.4\r\n<\/pre>
\r\nD =\r\n\r\n  4×4 logical array\r\n\r\n   1   1   0   0\r\n   1   0   0   0\r\n   0   0   0   0\r\n   0   0   0   0\r\n\r\n<\/pre>
If we use D<\/tt> as an index into C<\/tt> with the expression C(D)<\/tt>, then we will extract all the values of C<\/tt> corresponding to nonzero values of D<\/tt> and returns them as a column vector. It is equivalent to C(find(D))<\/tt>.<\/p>
C(D)\r\n<\/pre>
\r\nans =\r\n\r\n    1.0000\r\n    0.5000\r\n    0.5000\r\n\r\n<\/pre>
Now we know enough to break down the B(isnan(B))<\/tt> expression to see how it works.<\/p>
B = rand(3,3);\r\nB(2, 2:3) = NaN;\r\n\r\nnan_locations = isnan(B)\r\n<\/pre>
\r\nnan_locations =\r\n\r\n  3×3 logical array\r\n\r\n   0   0   0\r\n   0   1   1\r\n   0   0   0\r\n\r\n<\/pre>
B(nan_locations)\r\n<\/pre>
\r\nans =\r\n\r\n   NaN\r\n   NaN\r\n\r\n<\/pre>
B(nan_locations) = 0\r\n<\/pre>
\r\nB =\r\n\r\n    0.0292    0.4886    0.4588\r\n    0.9289         0         0\r\n    0.7303    0.2373    0.5468\r\n\r\n<\/pre>
Functions in the Image Processing Toolbox, as well as the MATLAB functions imread<\/tt> and imwrite<\/tt>, follow the convention that logical matrices are treated as binary (black and white) images.  For example, when you read a 1-bit image file using imread<\/tt>, it returns a logical matrix:<\/p>
bw = imread('text.png'<\/span>);\r\nwhos bw<\/span>\r\n<\/pre>
  Name        Size             Bytes  Class      Attributes\r\n\r\n  bw        256x256            65536  logical              \r\n\r\n<\/pre>
This convention, together with logical indexing, makes it very convenient and expressive to use binary images as pixel masks for extracting or operating on sets of pixels.<\/p>
Here's an example showing how to use logical indexing to compute the histogram of a subset of image pixels. Specifically, given a grayscale image and a binary segmentation, compute the histogram of just the foreground pixels in the image.<\/p>
Here's our original image:<\/p>
I = imread('rice.png'<\/span>);\r\nimshow(I)\r\n<\/pre>\"\" 
Here's a segmentation result (computed and saved earlier), represented as a binary image:<\/p>
url = 'https:\/\/blogs.mathworks.com\/images\/steve\/192\/rice_bw.png'<\/span>;\r\nbw = imread(url);\r\nimshow(bw)\r\n<\/pre>\"\" 
Now use the segmentation result as a logical index into the original image to extract the foreground pixel values.<\/p>
foreground_pixels = I(bw);\r\nwhos foreground_pixels<\/span>\r\n<\/pre>
  Name                       Size            Bytes  Class    Attributes\r\n\r\n  foreground_pixels      17597x1             17597  uint8              \r\n\r\n<\/pre>
Finally, compute the histogram of the foreground pixels.<\/p>
figure\r\nimhist(foreground_pixels)\r\n<\/pre>\"\" 
As another example, you could complement the binary image to compute something based on the background pixels.<\/p>
imhist(I(~bw))\r\n<\/pre>\"\" 
PS. I expect that this will be the last blog post that I write using R2016b. Keep an eye on the downloads page!<\/a><\/i><\/p>