Re: Fuzzy Life

WSiler (wsiler@aol.com)
Mon, 11 Jan 1999 06:59:36 +0100 (MET)

>Does anyone know of a "fuzzy" version of Conway's Life or any other
>cellular automata that function under a continuum state rule? (Meaning
>that a cell is "completely dead" when its value is zero, "completely
>alive" when its value is one, etc.)

No problem. Suppose, for example, we have a noisy gray-scale image. We would
like to reduce the noise. We pick a little cell automaton to do this. We will
simply reset the value of a pixel to the average of those within a small
neighborhood. We set up a loop in which i and j are a pixel's coordinates, and
pixel[i][j] is its value. newPixel[i][j] will be the modified image.

for ( i = 1; i < imax; ++i)
{
for (j = 1; j < jmax; ++j)
{
avg = 0;
for (deltaI = -1; deltaI <= 1; ++deltaI)
for (deltaJ = -1; deltaJ <= 1; ++deltaJ)
avg = avg + pixel[i + deltaI][j+deltaJ];
}
}
newPixel[i][j] = avg / 9;

Of course, this is pretty simple-minded. We might want to set a threshold for
the difference between a pixel's value and the average, and not change the
pixel's value unless the difference is greater than our threshold. We might
want to move the pixel's value closer to the average, but not simply reset it.
We might want to iterate the loop with a termination criteria put in. We might
want to convert the image to a binary one, and simply switch the pixel's value
to max if it is greater than the average, or zero if it is less than the
average. And so on.

We have used this type of algorithm (iterated) with success on noisy gray-scale
echocardiogram images of the beating human heart as a segmentation device, part
of a fuzzy expert pattern recognition system. Our system, usithe fuzzy expert
system shell FLOPS, won first prize at an international Cardiology conference
about 12 or 15 years ago.

William Siler

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