# Lookup tables for binary image processing—makelut and applylut

This is the second in a short series on using lookup tables for binary image neighborhood operations. See the first post for the basic idea.

The Image Processing Toolbox has two related functions:

• applylut - Process binary image using lookup table
• makelut - Utility function to help you construct a lookup table.

Since you have to have a lookup table in order to use applylut, let's start with makelut. It's syntax is:

 lut = makelut(f, n)

f is a function handle, and n is either 2 or 3, depending on whether your lookup table is to be used with 2-by-2 or 3-by-3 neighborhoods.

For 3-by-3 neighborhoods, makelut will call your function handle f 512 times. In each call, makelut will pass as an argument to f one of the 512 possible 3-by-3 binary neighborhoods. f simply has to return the desired output value for a given neighborhood.

For example, suppose we want the output pixel to be 1 if and only if the corresponding input neighborhood looks like this:

  1 0 0
0 1 0
0 0 1

The you would call makelut as follows:

pattern = [1 0 0; 0 1 0; 0 0 1];
lut = makelut(@(neighborhood) isequal(neighborhood, pattern), 3);
size(lut)
ans =

512     1



Let's try that on a small sample image.

bw = eye(5) | fliplr(eye(5))
bw =

1     0     0     0     1
0     1     0     1     0
0     0     1     0     0
0     1     0     1     0
1     0     0     0     1


bw2 = applylut(bw, lut)
bw2 =

0     0     0     0     0
0     1     0     0     0
0     0     0     0     0
0     0     0     1     0
0     0     0     0     0



So we see that only two input pixels, (2,2) and (4,4), have neighborhoods that exactly match the pattern.

Here's another example: Find all "endpoint" pixels. I'll define an endpoint pixel as a foreground pixel with exactly one foreground neighbor.

endpoint_fcn = @(nhood) (nhood(2,2) ~= 0) && (sum(nhood(:)) == 2);
endpoint_lut = makelut(endpoint_fcn, 3);

Here's the result on sample image from above:

bw3 = applylut(bw, endpoint_lut)
bw3 =

1     0     0     0     1
0     0     0     0     0
0     0     0     0     0
0     0     0     0     0
1     0     0     0     1



Only the four corner pixels are endpoints.

In my next post on this topic, I'll use makelut and applylut to play Conway's Game of Life. Look for it in a week or so.

Published with MATLAB® 7.6

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