Logical Indexing Example
From MATLAB Techniques for Image Processing by Steve Eddins.
Contents
Every MATLAB user is familiar with ordinary matrix indexing notation.
clear A = magic(5)
A = 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9
A(2,3)
ans = 7
A(2,3) extracts the 2nd row, 3rd column of the matrix A. You can extract more than one row and column at the same time:
A(2:4,3:5)
ans = 7 14 16 13 20 22 19 21 3
When an indexing expression appears on the left-hand side of the equals sign, it's assignment:
A(5,5) = 100
A = 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 100
About every 13.6 days, someone asks this question on comp.soft-sys.matlab:
How do I replace all the NaNs in my matrix B with 0s?
This is generally followed 4.8 minutes later with this reply from one of the newsgroup regulars:
B(isnan(B)) = 0;
For example:
B = rand(3,3); B(2,2:3) = NaN
B = 0.2122 0.1750 0.8944 0.0985 NaN NaN 0.8236 0.6660 0.7027
Replace the NaNs with zeros:
B(isnan(B)) = 0
B = 0.2122 0.1750 0.8944 0.0985 0 0 0.8236 0.6660 0.7027
The expression
B(isnan(B))
is an example of logical indexing. Logical indexing is a compact and expressive notation that's very useful for many image processing operations.
Let's talk about the basic rules of logical indexing, and then we'll reexamine the expression B(isnan(B)).
If D is a logical array, then C(D) is a logical indexing expression.
"Logical" is one of the builtin types, or classes, of MATLAB matrices. Logical operators, such as == or >, produce logical matrices.
C = hilb(4)
C = 1.0000 0.5000 0.3333 0.2500 0.5000 0.3333 0.2500 0.2000 0.3333 0.2500 0.2000 0.1667 0.2500 0.2000 0.1667 0.1429
D = C > 0.4
D = 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
whos
Name Size Bytes Class Attributes A 5x5 200 double B 3x3 72 double C 4x4 128 double D 4x4 16 logical ans 3x3 72 double
You can see from the output of whos that the class of the variable D is logical. The logical indexing expression C(D) extracts all the values of C corresponding to nonzero values of D and returns them as a column vector.
C(D)
ans = 1.0000 0.5000 0.5000
Now we know enough to break down the B(isnan(B)) example to see how it works.
B = rand(3,3); B(2,2:3) = NaN; nan_locations = isnan(B)
nan_locations = 0 0 0 0 1 1 0 0 0
whos nan_locations
Name Size Bytes Class Attributes nan_locations 3x3 9 logical
B(nan_locations)
ans = NaN NaN
B(nan_locations) = 0
B = 0.1536 0.6797 0.7486 0.9535 0 0 0.5409 0.8092 0.5250
Connection to binary images
Functions in the Image Processing Toolbox, as well as the MATLAB functions imread and imwrite, 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, it returns a logical matrix:
bw = imread('text.png'); imshow(bw) whos bw
Name Size Bytes Class Attributes bw 256x256 65536 logical

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.
Example: Histogram of foreground pixels
Given a gray-scale image and a binary segmentation, compute the histogram of just the foreground pixels in the image.
Here's our original image:
I = imread('rice.png');
imshow(I)

Here's the segmentation result (computed and saved earlier), represented as a binary image:
bw = imread('segmented_rice.png');
imshow(bw)

Now use the segmentation result as a logical index into the original image to extract the foreground pixel values.
foreground_pixels = I(bw);
whos foreground_pixels
Name Size Bytes Class Attributes foreground_pixels 17679x1 17679 uint8
Finally, compute the histogram of the foreground pixels.
figure imhist(foreground_pixels)

Or use logical indexing with the complement of the segmentation result to compute the histogram of the background pixels.
imhist(I(~bw))
